Lamarck Was Right

"Jean-Baptiste Lamarck: What I am saying is that basically, the inheritance of acquired traits change a species over time. Georges Cuvier: And what I am saying is no, that is the stupidest thing anyone has ever heard of."

- Hark! A Vagrant, "In Theory, Your Theories Could Be Sexier"

In The Golden Age of Comic Books, there were well established ways for a character to gain his or her powers: being bitten by a radioactive spider, doing years of Charles Atlas training, having a near-death experience, extensive mystic training, getting an artifact of great power, being disgustingly wealthy, and scores of other imaginative backstories. With the advent of the Silver Age onwards, these Golden Age heroes had children. Naturally, they inherited their parents' powers and heroic tendencies and many became legacy characters, through the sometimes magical agency of Superpowerful Genetics.

Um. Okay. We'll make that deal, for the sake of story.

Tough to see, though, how training is inherited, or how body-mods get passed on. Pretty good chance that any kid that Iron Man might have had would not have been born with rivets.

If the comic or show is rife with My Kung Fu Is Stronger Than Yours, then the superkid will luck out and be at least as powerful as the strongest parent at the time of conception, and often radically more powerful. This can get interesting if a family has more than one kid, as each succeeding one gets stronger. This usually also applies to fighting skills; they'll be a prodigy black belt before they can walk. If the parent got their powers from a magical or technological artifact, they'll have "internalized" and passed on that item's power. To use a real world analogy: if your mom were an IT expert that always carried around a laptop, you'd have a Bluetooth connection in your head and know how to code a Linux kernel from scratch.

Other times, if the parent got their power from a Freak Lab Accident involving Applied Phlebotinum, their children will all have that same power, regardless of whether it affected their DNA. This also applies to magic and telepathic powers. Of course, with magic, the reason it's passed down will frequently be less biological than spiritual, so the usual rules need not apply. Another real-world analogy: If your dad were a food tester who developed a high tolerance for poison through controlled exposure, you'd have his high resistance and then some. This one is often retconned into a Meta Origin or Secret Legacy; for instance, maybe the accident didn't cause your dad's powers, it just unlocked the powers already in his DNA, and he passed the "unlocked" version on to you -- and note that this is real science.

This trope is named for Jean-Baptiste Lamarck, a French naturalist whose theories (of which we call Lamarckian evolution) inspired Charles Darwin and eventually led to modern Darwinian evolution. While very insightful, his theory of "Inheritance of Acquired Traits" incorrectly viewed the cause of evolution as the parents' self-improvements in life being passed on to their offspring. Giraffes had long necks because they kept stretching for higher branches over many generations, for instance. While this idea has become closely linked to Lamarck, it was not original to Lamarck, nor was it central to Lamarck's contribution to evolutionary theory.

There is a real world phenomenon known as the epigenome, that describes how the DNA expression if not actual DNA can be affected by environmental factors in the lives of ancestors. For instance, famines at certain stages in the lives of grandparents can adjust the rates of diabetes in the grandchildren. Hank Green briefly explains the relatively new field of epigenetics in this YouTube video.

A.k.a. Inheritance of Acquired Traits. See also Evolutionary Levels and Superpowerful Genetics. Compare In the Blood for the morality version. Generation Xerox is this trope Up to Eleven; the kids inherit more than just their parent's physical traits. Sub-Trope of All Theories Are True. Muggle Born of Mages is the Subversion. Randomly-Gifted is an Aversion.

Anime & Manga

 * Everyone in the Fullmetal Alchemist world knows: (ahem...) THIS HAIR CURL, THESE MUSCLES, THESE PINK SPARKLES, THIS GREATCOAT, THIS ALCHEMY AND THIS Badass Mustache HAS BEEN PASSED DOWN THE ARMSTRONG LINE FOR GENERATIONS!!!
 * It's never outright stated, but Dragonball Z implies that Goten and Trunks can reach Super Saiyan at a young age because their fathers had achieved the level before the boys' birth; compare to Gohan, born before Goku ever became a Super Saiyan, and had to earn it the same way his father and Vegeta did. This was apparently a major source of fan contention, since some viewers took a cue from Vegeta and complained it took away from the mythos of how becoming Super Saiyan was supposed to be incredibly difficult.
 * An alternate fan theory is that they achieved it so quickly because nobody ever told them it was supposed to be hard.
 * And of course, GT takes this to the extreme in the final episode by showing distant descendants of Goku and Vegeta (identical grandsons, actually) can achieve Super Saiyan without even realizing the significance of it.
 * Goku implied at one point that the generations after his and Vegeta's are stronger because the enemies they've had to face were much more powerful; Gohan was strong enough to fight Cell at eleven, while Goku at that age was still frolicking in the forest.
 * The eponymous power-granting brain parasite of Baoh the Visitor was artificially evolved through the use of a serum that causes Lamarckian evolution. Animals injected with the stuff are deliberately placed in extremely harsh environments, adapt to them, and pass on their adaptations to their offspring, then the next generation is injected and the cycle repeated until something interesting and weapon-ish is produced, leading to the Baoh worm and other rather random creations.
 * In Historie, Eumenes is not only naturally intelligent, but.
 * We never get to see it in the manga, but according to the author, Kenshin's son, Kenji, manages to master the Hiten Mitsurugi-Ryū style of kendo all by himself, without having ever seen it and figuring it out from mere descriptions, because his father refuses to pass it down to him.
 * In Baccano!, Huey Laforet, immortal thanks to the Elixir of Life, sires Chane for the purpose of testing this trope. Turns out that Lamarck Wasn't Right.
 * In Shaman Warrior,
 * Mahou Sensei Negima toys with this one, as Negi aspires to be just like his father Nagi, the most powerful mage ever. Negi himself turns out to be a prodigy, but his strength comes from his intelligence and constant training, whereas his father was a complete idiot but so naturally powerful that he was practically invincible anyway.
 * Lately though its looking like Negi takes after his mother a lot more than he does his father:
 * ...and then there is who might be playing with this trope (how directly though hasn't been seen yet).
 * Pokémon Special: Amazingly enough, this is actually Gold's special ability. He can pass his will to an unhatched Pokémon. His Togepi turned out to be a avid gambler with a violent temper because its owner carried its egg around arcades and dreamed about it beating the crap out of Silver. His Pichu also turned out to be super-powerful and brave because he wanted to protect it and prove himself worthy of being a Dex Holder.
 * In the Pokémon anime, it's stated that Pokémon can see and hear through their eggs, but it's unknown if this extends to any other continuity.
 * In Bleach it was recently revealed that.
 * A late manga story arc of Ranma ½ introduces the Musk Dynasty, who use magic to bring about this precise effect and are one part Villain of the Week to one part Wacky Wayside Tribe. Generations ago, the Musk's ancestors were a group of martial artists who wanted to become the greatest masters of the various "Animal Styles" of Kung Fu. So, they settled in a valley near Jusenkyô, crafted two magical items to enable or disable Shapeshifter Mode Lock, and took to capturing animals, cursing them in the Spring of Drowned Girl, locking them in that form, and having kids with them to ensure that the children would gain the traits of their moms' original species and thus be natural masters of the related style. It seems to have worked; Herb, a dragon-blooded, is an incredibly powerful ki user, the tiger-blooded Lime is a Mighty Glacier and wolf-blooded Mint is a Fragile Speedster. However, it also seems to have done a number on their mental abilities, which may be why that Herb says they gave up the practice some time ago. While the sheer misogony of their lifestyle may be partially to blame (Musk boys are taken from their mothers once they're weaned and don't have any contact with the opposite sex until it's time for them to marry), Mint and Lime are dimwitted and girl-obsessed, to the point of openly fantasizing about holding hands with girls, touching or seeing breasts, and literally grabbing girls in the middle of the street to try and make these dreams come true. And Herb, though generally smarter, was still dumb enough to take the Locking Ladle with him to Jusenkyô; when he turned a monkey into a girl to be able to see what a woman's body looked like before he got married. Even though he only intended to have the monkey-girl around for a few moments and just let her run off afterwards. Naturally, this gets him a Gender Bender curse and stuck in female form to boot, forcing him/her to come to Japan to get it fixed.

Card Games
"Each new generation of slivers evolves to assimilate the strengths of the prey upon which their progenitors fed."
 * In Magic: The Gathering, evolution seems to work this way. A telling example:

Comics

 * Alan Scott, the original Green Lantern, had a daughter called Jade, who naturally had all the powers of his ring, and occasionally her mother's plant powers as well. He also has a son who has darkness-related powers, which are explained as Alan having been exposed to "Shadowlands energy" during a fight with a demon.
 * Although, after multiple reboots and retcons, Alan Scott's power base ended up magical, so a Wizard Did It.
 * Man-Bat gained bat-themed powers artificially but his daughter inherited them. When consulted about this, Batman was skeptical, and explicitly said that acquired characteristics can't be inherited (despite the number of times that exactly that has happened in the DCU).
 * The "Battle For The Cowl" miniseries/crossover began to fix that. Another villain points out to Langstrom that it's impossible for a mix of common chemicals to have that effect, that the formula was a psychological crutch for the activation of Langstrom's innate super-powers. And indeed, in that same issue he manages to transform without the formula and keep control (to a degree).
 * Which didn't actually make any sense, considering this was maybe a year after Talia al-Ghul managed to steal the formula and use it create an army of ninja Man-Bats.
 * A mainstay of the Marvel Universe, where everything from Spider-Man's radioactive spider bite to the Fantastic Four's cosmic ray exposure can be inherited. Generally, it's revealed that the various doses of radiation did change their DNA, so the offspring of Freak Lab Accident Silver Agers can officially be called Mutants.
 * The official Marvel parlance is Mutants for X-gene variations on the human template, and mutates for those like Spider-Man who've been mutated by some external factor. How the public magically tells the difference is another question altogether.
 * Two Flashes -- Wally West and Barry Allen -- have had children, and in both cases the children have inherited the speed powers. It's a Speed Force thing, or something. It's even bred true to both of Barry's grandkids.
 * Indeed, Barry Allen's grandson's half-brother also has speed powers, although neither of his parents ever did. Also, as the son of Captain Boomerang, he's inherited his father's knack for using boomerangs as offensive weapons..
 * On the other hand, Owen and Bart's mother, Meloni Thawne, is a descendant of Barry's twin brother, Malcolm Thawne, as was Eobard Thawne, AKA Professor Zoom, which suggests that the Barry Allen bloodline has a genetic predisposition toward speed, rather than a Lamarkian outgrowth from Barry's.
 * Which can further be explained by the fact that Barry Allen might have been the creator of the Speed Force, and so anybody else in his bloodline will have a higher chance of inheriting speed based powers. Of course, Barry's powers themselves are an ontological paradox, as it's been stated in the comics that he went back in time, turned into a bolt of energy, and struck the chemicals which gave him superspeed.
 * Double Subverted with Wildcat II, the son of Wildcat. Wildcat is a superb fighter with no other powers. His son isn't so great at it. On the other hand, after the father spent a lifetime of dressing up in a cat suit, the son can turn into a Catboy. As it turns out, his powers really are inherited - his mother was a werepanther, so it's just an amusing coincidence that his power connected with his old man's gimmick.
 * Scarlet and Sheena Hellpop inherited their father's fusionkasting powers, even though his abilities were given him by the Merk, and were also periodically taken away.
 * The Zenith series in 2000 AD relied on this. The main strand of superhumans in the story were able to pass on their superpowers to their offspring. Their powers originated in a wartime experiment where pregnant women were injected with ergot alkaloids. The resulting children's superpowers were mentally derived, you see, and kicked in when the children hit puberty.
 * The character Doomsday was created deliberately through a brutal process of Lamarckian evolution.
 * Alternatively, given the vast number of mutations that occur within individual cells in the human body, the researchers could have simply been playing a genetic lottery each successive cloning generation.
 * The children of characters in the Marvel Universe having similar powers are usually explained as "mutants" of some kind due to their progenitors' exposure to the weird. For example, Spider-Girl is the daughter of Spider-Man, even though his powers came from an outside source when he was in his teens. So too is Franklin Richards; both his parents were altered by cosmic rays and became empowered. However, taking the cake is probably Rachel Summers, daughter of Jean Grey, who was a mutant of impressive power and a wielder of the Phoenix Force. While it now makes sense, sort of, when she was first introduced, the Phoenix Force was a power that came to beings and could even leave them, as opposed to being a permanent change. Somehow, Rachel inherited that. Being the White Phoenix is kind of Jean Grey's mutation now, but not quite, so it almost makes sense, but somehow falls short. Apparently the Phoenix (which is a sentient entity in its own right) just likes fusing with members of the Grey-Summers lines.
 * It probably has something to do with the sheer power of the Phoenix Force. It can't inhabit most people, but it can inhabit Jean Grey due to her insane level of psionic power. And, as was made obvious by Sinister for like the last fifty years, all the children of Scott and Jean tend to inherit their mother's power and then some.
 * In Spider-Man's case, the bite changed him on a genetic level, so it would make sense for any children of his to inherit his powers. And to be fair, Spider-Girl's powers aren't an exact copy of Peter's, there's a major difference in how their wall-crawling powers work.
 * Kara Killgrave (a.k.a. Purple Girl, Persuasion, Purple Woman), the daughter of the Purple Man, is another case, as she developed the exact same powers as her father, right down to his purple skin. That's despite the fact that he was hit by a rapidly-escaping nerve gas.
 * Marvel character Scorpion (Carmilla Black) was designed based on the original plan that she was the daughter of Viper (Madame Hydra). To show she was Viper's daughter they gave her naturally green hair -- which would only be possible if hair dye is hereditary. Granted, they ended up with Monica Rappaccini (AIM Leader) as her mother.
 * It's since been suggested Scorpion's father might be Bruce Banner as an explanation for her green hair. Since this would have been before Banner became the Hulk, this just raises further questions.
 * Speaking of Dr. Banner, he's had three children post-Hulk. His daughter Lyra has green skin and some super-strength, but averts the trope because she was created via genetic engineering. His son Skaar is able to become a Hulk himself, while his twin Hiro-Kala appears to have inherited nothing of the Hulk (implying they're likely fraternal twins).
 * Captain America (comics) received his powers (physical attributes at the absolute peak of human perfection) from a shot of the Super Soldier Serum; after that the serum was tested on black soldiers, and of the initial test subjects, only Isiah Bradley survived, gaining the peak physicality. Bradley's son, Josiah, inherited the Super Soldier Serum effects from his father. He uses the name Josiah X in his hero career. Bradley's grandson, Elijah Bradley, gets seriously injured when the Skrulls attack New York, and after a blood transfusion from his grandfather, gained the traits of Captain America. This is somewhat better than the standard explanation.
 * In the Ultimateverse, Cap's son inherits superpowers. The son, however, appears to be better with them than Cap ever was, mostly because of training from a young age.
 * While not really offspring, The Joker manages to "Jokerize" scores of supervillains in The Last Laugh storyline. He does this via some insane Evil Plan that infuses everyone with his DNA, turning their skin white, hair green and giving them Joker's sense of humor and making them totally loyal to him. How this works when the Joker's skin and hair color is not due to any sort of genetics but his skin and hair being permanently bleached from (in the usual backstories) falling into a vat of chemicals is not explained.
 * For that matter, how does being "totally loyal to him" qualify as one of the traits in Joker's DNA? He's chaos embodied, the polar opposite of loyalty.
 * Similarly, a Batman vs Aliens comic featured a mad scientist infusing xenomorphs with the DNA of Batman's villains. Not only did one of them develop white skin and red lips, another developed scarring on the left side of its head and a third somehow acquired the colouring of Scarecrow's costume.
 * Avengers Academy character Finesse has the same powers as Taskmaster, who gained them by special serum, and it's implied she might be his daughter. When the two of them meet, she directly asks him about it, only for it to turn out that a drawback of his powers is loss of his non-combat related memories, so he has no damn idea.
 * One What If story had the heroes getting trapped in Battleworld after the events of Secret War, settling down and having children. All the kids have combinations of their parents' powers and traits; Captain America (comics) and Rogue 's daughter has strength, flight, and is a natural leader, while Human Torch and Wasp's son has Hot Wings and fire projection (but only when he's shrunk) and is a smartass.

Films -- Live-Action

 * In the movie version of A History of Violence, Viggo Mortensen's character Tom Stall has the titular violent history along with wicked underhanded fighting skills. After his abilities are outed, his previously passive and somewhat defensively-snarky son (who had up to this point been in a healthy and loving environment, in which Tom preached self-control) went off like a claymore mine on a bully, beating him down with surprising savagery. However, it is mostly the surprise that won him the fight; the temper may have been his father's (such things may be inherited), and he showed no real technique, so this is a borderline example.
 * Likewise, in August Rush, the titular character is a musical prodigy whose biological parents were both musicians. Now, musical aptitude can be inherited. Not prodigy-level, but...
 * Lampshaded in Sky High, with a lecture on superhero genetics given by the school nurse.
 * In Indiana Jones and the Kingdom of the Crystal Skull,, Mutt suddenly displays miraculous rope-swinging powers.
 * He does swing every bit as well as the monkeys in the jungle around him...
 * In The Legend of Zorro, Don Alejandro de la Vega's son, Joaquin, seems to have inherited his father's taste for social justice and swordfighting skills despite the fact that he has no idea his father is actually Zorro.
 * Somewhat related instance in Alien: Resurrection, where centuries after the third movie, scientists clone Ripley, complete with the parasite infecting her when she died. However, the failed clones make it evident that the Xenomorphs invade their hosts at a genetic level which was already implied in the last movie. Bonus points for the Xenomorphs' "genetic memory" which allows Ripley to remember her past life, though she does suffer from autism and other problems. Considering that the screenwriter was instructed to include Ripley's character in the film, this all comes off as remarkably plausible for a science-fiction action movie.
 * Boondock Saints: The brothers are extremely skilled at using firearms; but no mention is made of them having formal or informal military/firearms training. Their father is just as gun-crazy and vigilante-minded; but spent the entirety of his sons' lives in jail. It is lampshaded in the second movie, when the Big Bad comes right out and states that killing runs in their blood.
 * While it is never explicitly stated that the McManus brothers have had any specialized training; the first movie hints strongly that they were given some sort of training at their mother's insistence (this is explicitly stated regarding their polyglotism), as well as hinting strongly at ties to Irish Republican organizations. The second movie does invoke this trope, but it's a fairly weak example in context.
 * In Pandorum, the colonists were injected with mutagens designed to make them undergo "accelerated evolution". Unfortunately it caused those who woke up first (or maybe their descendants) to become albino cannibals.

Folklore

 * One Cherokee creation myth states that originally, all the world's deer lived in a single cave. When a boy who wanted to hunt them unsealed the cave, they all ran out. The boy quickly shot them all as they fled, but they survived and he only managed to hit them in their anuses, because they were running away. As a result, they lifted their tails up. Supposedly, this is why deer keep their tails pointed up to this day.
 * A European folktale says that the reason dogs have wet noses is that the two dogs on Noah's Ark spent the Great Flood with their noses sticking out in the rain.
 * There are similar tales on why bears have short tails (ice fishing with their tails, getting most of it bitten off by a pike/frozen off by the cold water) and why elephants have trunks (getting too close to a crocodile who grabbed his nose and ended up stretching it before the elephant managed to struggle free).
 * Similarly, the tale of Loki's final capture and binding until Ragnarok told of how he tried to escape the Aesir's wrath by turning into a salmon and swimming away. Thor caught him by the tail, squeezing with godlike strength. This is the Norse explanation for salmon having pointed tails.
 * There are countless tales that explain how a certain animal became what it is, all via artificial means. Be it a certain color they received via paint being dropped on them (like one bird which is very colorful, supposedly cause God was running out of paint and used a bit of everything on the last bird), body "deformations" due to mechanical force (like the elephant example above), losing body parts due to them being chopped off, or behaviors which are supposedly due to past experiences (e.g. the reason all birds are hostile towards owls is supposed to be because the owl messed something up in one folklore, so it seems even grudges get inherited.)
 * Siamese cats supposedly have kinked tails because their ancestors used to hold the rings of their ancient Siamese princess owners on their tails while the women would bathe, and the cats would then helpfully curve the tails to hold the jewelry better.
 * Genesis suggests that men have one less rib than women because God took a rib from Adam to create Eve. (This isn't the case; men and women have the same number of ribs.)
 * The "adam's apple", almost always more prominent in men, is named so after people assumed it came from a piece forbidden fruit that got caught in Adam's throat.
 * Arguably, the snake which God cursed for having caused Adam and Eve to eat the forbidden fruit, dooming it to "crawl on its belly for the rest of its days" (implying it moved some other way before). Of course, God being who he is, he could have easily changed the snake's DNA around if he felt like it.
 * According to Japanese folklore, a sleeping cat once had its tail catch on fire, and it ran, panicked through a city, burning the entire place to the ground. Henceforth, the emperor himself declared that all cats have their tails docked short, explaining why the Japanese bobtail breed has a short tail.

Literature

 * Discworld
 * Soul Music: Susan Sto Helit is Death's granddaughter, and has much of his power. The problem is, Susan's mother was Death's adopted daughter; her father was Death's apprentice. She also has a mark on her cheek that resembles the mark her father got when he was slapped by Death. Susan lampshades this by repeatedly pointing out genetics does not work that way. The series itself, meanwhile, has noted that on the Disc, not all heredity is genetic.
 * Conina from Sourcery. She is the daughter of Cohen the Barbarian -- and frustrated by her constant urges to dress in skimpy animal skins and beat the crap out of everyone that looks at her the wrong way. She's also inherited his Charles Atlas Superpower.
 * The passing of skills along family lines is explained within the religious underpinnings of Nancy Farmer's The Ear, the Eye, and the Arm: The spirits of your ancestors actually hung around the family, and if they took a liking to a kid, they'd pass down their own skills. Hence, if little Jimmy winds up with unbelievable skills at piloting a fighter plane, it's not so much because he's genetically related to great-great-grand-uncle George (the ace fighter pilot), but because George's spirit stuck around after death, and kinda melded with Jimmy to grant him George's original powers.
 * In Harry Potter, Harry instantly becomes a talented Seeker despite never having played or even seen anyone play before. The characters explain this by saying that James was an incredible flyer as well.
 * Justified somewhat considering Harry had ridden a practice broom at a young age, and technically only inherited good flying skills and reflexes, which can be from genes. (Though the reflexes he claims come from dodging his bully cousin Dudley.)
 * The problem here stems from the fact that it is said that Harry got his good eyesight for locating the snitch from his father. The same Harry that wears glasses...
 * In the Shannara book series, the Ohmsford family begins to have innate magic starting with the children of Wil Ohmsford. Justified in-story: Wil's use of the magical elfstones was problematic, as he wasn't "elf" enough, and permanently left a trace of magic within him.
 * In the novel 2001: A Space Odyssey, the man-ape Moon-Watcher being made intelligent by the monolith is described thus: "The very atoms of his simple brain were being twisted into new patterns. If he survived, those patterns would become eternal, for his genes would pass them on to future generations." If the monolith wanted the patterns passed on, it should have been doing the twisting a bit lower down...
 * Rudyard Kipling evidently believed in Lamarckian evolution. In "Kaa's Hunting" Mowgli is able to show the monkeys his skill at weaving sticks together because he is a woodcutter's son, while in "Red Dog" he cuts off the leading red dog's tail and then taunts him by telling him "There will now be many litters of little tailless red dogs, yea, with raw red stumps that sting when the sand is hot." (Since a wolf ends up killing him anyway this theory is never put to the test).
 * And, of course, all of the Just So Stories are pure Lamarck, justified a bit in that they are meant to be creation myths after all. Well, except how the camel got his humph but that's another tale entirely.
 * Tarzan's son inherited his father's highly trained strength, reflexes, and ability to understand animals (particularly apes).
 * In Frankenstein Frankenstein destroys the "bride" he created for the monster because he fears what might happen if they reproduced. Frankenstein was written before either Lamarck's or Darwin's theories were proposed. In short, Science Marches On.
 * In Fred Saberhagen's The Frankenstein Papers, the greedy plantation-owner funding Frankenstein's research expects the trope to hold. He expects his creations will breed a new race of super-strong laborers to work as slaves on their Caribbean properties. No such luck.
 * In Mike Resnick's Widowmaker series, the main character is the most lethal fighter in the galaxy but contracted a disease with no cure. He had himself frozen until a cure can be found but due to maintenance expenses, the doctors unfreeze him to make bounty hunter clones. The clones have his memories and skills but have subtle (sometimes) differences.
 * In Agatha Christie's short story "The Cretan Bull" in her collection The Labors of Hercules, Hercule Poirot solves a mystery by determining that the character Colonel Frobisher was really the father of Hugh Chandler. He did this due to the biological fact that Hugh inherited Frobisher's habit of "drawing down his brows over his eyes and lowering his head, thrusting it forward, while those same shrewd little eyes studied you piercingly." No word which chromosome this habit comes from.
 * Runs rampant in the 4th book of Twilight. Try not to think about it too hard.
 * In the story Bisclavret from the Lais of Marie de France, a werewolf bites off a woman's nose and all of her descendants are born without noses because of that.
 * Justified in the SF short story The Engineer and the Executioner, about a genetic experiment in a hollowed-out asteroid (which is actually called Lamarck), as the colony used in the experiment was actually designed to use Lamarckian evolution (which, in the story, turns out to be astonishingly rapid).
 * In the sequel to Wicked, Son Of A Witch,
 * Oddly abused in Brandon Sanderson's Alcatraz vs the Evil Librarians YA novels, where superhuman powers, called "Talents," seem to come from having the last name "Smedry". Al's mother.
 * The novelization of A New Hope averts this. Ben comments that like his father, Luke is an excellent pilot, then goes on to say that "[p]iloting skill isn't hereditary, but many of the aptitudes that produce a good small-ship pilot are." It's also established that Luke's spent a lot of time practicing high-speed low-altitude high-precision flying.
 * In Stephen King's Firestarter, a couple gains Psychic Powers (Mind Control and Telekinesis, respectively) from a drug given to them in an experiment. Their daughter is born with telekinesis and pyrokinesis as a result. This is Handwaved when the father speculates that the drug must have affected their DNA. King mentioned afterwards that he never liked that explanation, preferring stories where supernatural things just happen, and are never explained.

Live-Action TV

 * The Goa'uld in Stargate SG-1 are an entire species for which Lamarck Was Right. They even inherit memories. Since they are aliens with a very divergent reproductive cycle, human genetics doesn't apply. Less justifiable is that the child of two goa'uld hosts also inherits memories, despite being biologically human.
 * The commercials for Birds of Prey made a great deal out of the idea that the daughter of Batman and Catwoman would have inherited her father's drive to fight crime and her mother's drive to commit it. She also inherited cat-like abilities from her mother (who was a metahuman in the television show, despite her comic book Badass Normal characterization).
 * Used oddly in Psych where Gus insists that he can handle spicy (Indian) food because he's 1/4 Jamaican. His grandparent or parent may have cooked spicy Jamaican foods a lot, but it's not mentioned.
 * In a season two episode of Babylon 5, it is revealed that the PsiCorps have developed a treatment that turns telepaths into empaths, and that they want to subject Talia to the treatment and then have her get with the other empath to make lots of empath babies, proving that they are not only evil, they also Fail Biology Forever.
 * In Angel, Connor manages to inherit all the advantages of his vampire parents without actually being a vampire. How this works is never explained, but then, how two vampires had a baby in the first place is never explained either.
 * On The Mentalist, an internal affairs officer tells Lawful Good Fair Cop Rigsby it's not his fault if he's prone to crime, since his father was a biker, and evidence suggests criminality could run in the family. He is not happy. Also subverted in that everybody on the team is seen to be very different from their parents (who include the aforementioned biker, an abusive drunk, and a particularly nasty conman).

Music Videos

 * 2D of Gorillaz got his trademark blue hair when a head injury changed something in his brain chemistry, causing all his hair to fall out and grow back blue. In the old Kong Studios interactive website, there was an email on 2D's computer from a lawyer telling him he couldn't deny that his many illegitimate children were his because "the spiky blue hair is a dead giveaway".

Tabletop Games

 * Tieflings in the 4th Edition of Dungeons & Dragons have managed to partially inherit a Deal with the Devil that their ancestors made as a racial trait.
 * According to Draconomicon, dragons can pass on some of what they learn to their offspring. It's a handy way of ensuring they're Always Chaotic Evil.
 * In keeping with Gothic fiction, powerful curses in the Ravenloft setting can be passed down from one generation to the next, deserved or not. This may say more about the Dark Powers' Jerkass tendencies than about Lamarckism, however.
 * In GURPS 3rd Edition Steampunk sourcebook, optional rules are given if you want to play in a gameworld where Lamarckian evolution is correct, allowing high-skill parents to give exceptional talents to their offspring.
 * The Dragonbloods in Exalted benefit greatly from Lamarck being right, as do some mortals to a lesser extent. It stands out as being one of the few settings to have a god of Lamarck being right: Parad, the Left Hand of Power and God of Inherited Might.
 * This is shown by even having a background (merit trait) called "Breeding" which details the purity of blood and the elemental connection your parents possessed that you inherited.
 * Probably most prominent in the case of the children of powerful celestial exalted, given that the celestial's exaltations themselves are completely non-hereditary.
 * The Archeans, human-analogs from the Talislanta game, are descended from Beast Folk who'd used magic to eliminate their more animalistic traits. Justified in that, well, it's magic.

Video Games

 * Played straight in Phantasy Star III where at the end of each chapter, the main character can marry one of two girls. The kid will inherit the skills of his parents (including the capability of using magic) and some physical traits, including hair color.
 * Solid Snake of the Metal Gear series inherited, among other things, near-inhuman combat abilities and love of cardboard boxes from his "father" Big Boss. Metal Gear Solid even featured "Genome Soldiers" that were augmented by "gene therapy" with Big Boss's "soldier genes" in an effort to create elite soldiers without military training. It didn't work.
 * Romancing SaGa 2 had a system of inheriting the previous Emperor's abilities. Justified with magic, though.
 * This is one of the main reasons for breeding in Pokémon. The offspring will inherit certain moves from the father, and a lengthy "breeding chain" can be set up to get unique moves for Pokémon that wouldn't learn then normally.
 * The Ace Attorney series has this with
 * To a smaller degree, Franziska von Karma's inherited both her father Manfred von Karma's prosecuting skills and his
 * Maya, Mia, Misty and Pearl Fey have all inherited Ami Fey's potentital and ability to channel the spirits of the dead. Morgan Fey and her two other daughters, however, only got traces of it, which is a driving force behind a huge portion of the plot of the second and third games.
 * The Sonic the Hedgehog series' Chao (introduced in Sonic Adventure) work a little bit like this. Two Chao born as completely blank slates with randomized stat grades (indicating how well they're going to progress when that stat levels up) can raise their stats through work and even raise a stat's grade. If you breed them together, the child will inherit stat grades from one parent or the other and can inherit the improved grade rather than the original. Also its actual stats may be affected by its parents', I believe.
 * In Fire Emblem - Geneology of the Holy War (an untranslated Japan-only game for the SNES, which received an excellent Fan Translation... even if it isn't quite finished), the characters in the second generation (if their mother was paired up with someone) have their skills/stats/stat growths influenced by their parents. The Character Tiers take this into account.
 * In the games (in general), it's normally said that only certain bloodlines can use certain weapons. Examples include: the Falchion (FE 1/Shadow Dragon); Aum Staff (FE 1/Shadow Dragon) and all of the holy weapons (Genealogy of the Holy War).
 * Funnily enough, it's zigzagged in the Elibe saga; in The Blazing Blade, only Eliwood (descended from Roland) can wield Durandal and only Hector (implied to be Durban's descendant) can wield Armads. But Lyn and Hector are also descended from Roland, and neither of them can wield Durandal. And in The Sword of Seals, anyone skilled enough in swords or axes can wield Durandal or Armads respectively, and Roy (who is not descended from Hartmut) can wield the Sword of Seals. But nobody except Hartmut's descendants (read: Zephiel) can wield Eckeseax.
 * The Final Fantasy VII chocobo breeding sidequest relied partly on the birds' rankings in the chocobo racing minigame to produce Green, Blue, Black, and Gold chocobos with special powers.
 * The Asari from Mass Effect have an element of this. Essentially, because of the way their reproductive system works, it's theorised that the child develops traits that the "mother" really likes about the "father". It's not treated as fact, but more like a popular belief. Given the limited examples, however, the theory seems somewhat supported (though far from proven).
 * In the third game,  tells her that her grandfather was a Krogan, so it's perfectly understandable if she wants to head-butt somebody.
 * However  also lampshades the fact that, truthfully, no-one really knows how it works.
 * Minecraft takes this to extremes with livestock breeding. Sheep are usually white, but other natural colors include black, gray, brown, and (rarely) pink. However, sheep can be dyed any color of the rainbow, and this color is passed onto offspring. This feature was implemented by popular request, since blue dye is made from lapis lazuli, a mineral found deep underground, only slightly more common than diamonds.
 * Infinity Blade is this trope distilled into a video game. In it, the hero must defeat the evil God King, but will inevitably fail. No worries though, as his offspring inherits all XP and equipment from him, allowing the player to become stronger with each new generation.
 * In The Sims 3, parents can pass on their traits to their children. Also, since all hair/eye/skin colors are now equally dominant (opposed to following the basic Punnett model of dominant and recessive that was in its predecessor), you could easily have a child with Dad's blue skin and Mom's pink hair with orange highlights.
 * In Pokémon, T Ms learned by a parent pokemon are passed down to the children, as well as certain moves crossing species - a phenomenon referred to as "Egg Moves." Chain-breeding is how you achieve things like a Charizard which knows Crunch.

Web Comics
"Vaarsuvius: Heredity is a cruel mistress."
 * Parodied in this strip of The Last Days of Foxhound. The comic also has a lot of fun with its source material's love of this trope.
 * In Questionable Content, somehow a Roomba with a jet engine attached reproduced with another Roomba and had flying children. The Lamarckian inheritance is the least of our worries.
 * Twins Elan and Nale in Order of the Stick inherit multiple traits from their estranged parents. Elan adopts his Mother's Chaotic Good alignment and his father's love of the dramatic, while Nale adopts his Father's Lawful Evil tendencies and his mother's love of unnecessarily complex plans.

Web Original

 * Web prose series Star Harbor Nights has characters inheriting their parents' acquired as well as inborn mutations. Gleefully but obscurely Lampshaded by the name of a mutation-inducing drug, Lysenkol... named for Lysenko, a Soviet scientist who believed in the inheritance of acquired traits.
 * The Global Guardians PBEM Universe is an "unlimited source" setting, where superpowers can be gained through pretty much any possible way that can be imagined. Nevertheless, and regardless of what real-world genetic science says, its pretty much guaranteed that the child of two superhumans will have either the same powers as one of their parents, or a mix between the two. (Children with only one superhuman parent tend to have a 50/50 chance of getting either the same powers as their parents, or else no powers at all.) Of course, people who get their powers from technology don't count.
 * Something like this is going on in the Whateley Universe. Getting mutant powers is really really rare. But superheroes and supervillains seem to have insanely high odds of having kids with powers too. What, does using your powers a ton make them pop up in your kids?
 * Superpowers are explicitly a combination of genetic and environmental factors, super heroics probably come under environmental.
 * According to Word of God, the "mutant gene complex" is actually fairly common in the human population of Whateley Earth (about one in seven). It's that complex becoming active (usually at puberty) that's normally quite rare. Depending on how said complex gets passed on and what exactly triggers it, the chances of two "live" mutants who by definition both have it in their DNA themselves producing more mutant offspring could thus plausibly be quite high (non-mutant supers, however, are on their own).
 * Thoroughly deconstructed in Lamarckism Troubles.
 * Grandchildren of people who had lived through famine were less likely to catch diabetes. Mice exposed to enriched learning environments had offspring with improved memory This apparent Lamarckian inheritance is the third creepiest thing hiding in your DNA according to Cracked. This article also mentions endogenous retroviruses (see Real Life below).

Western Animation
"Gandhi: If there's one thing Mahatma Gandhi stands for, it's REVENGE!"
 * This idea is tossed around a bit in Avatar: The Last Airbender. If at least one of the parent is a bender, there's a good chance the child they have will also be a bender. Of course that's not including combinations from diffirent tribes and what not.
 * Subverted by Clone High, in which absolutely none of the clones have anything in common with their progenitors except for their appearance (and even that can be somewhat dubious; for instance, Cleopatra was not a beautiful native Egyptian, but descended from Greek rulers). The only one who even vaguely resembles their progenitor is JFK, who acts like a caricature of the actual Kennedy, due to a combination of insecurity over his masculinity due to his gay foster parents, and his belief that that's how the actual JFK acted.
 * Outright spoofed with Gandhi, who acts exactly how you wouldn't expect a clone of Mohandas Gandhi to behave; he's a loud, obnoxious, dim-witted skirt-chaser. Still non-violent, though. Sometimes.


 * Many of the minor clones really do act like their predecessors, though. This is mostly done for a quick gag (i.e., George Washington Carver's clone has somehow genetically engineered a talking peanut).
 * Famous 5: On The Case, the Disney cartoon based loosely on The Famous Five, plays this straight with the children of the original Five. Both boys have sons, both girls have daughters. Julian and his son Max are both action leaders, Dick and Dylan are both smart guys, George and Jo are tomboys, Allie and Anne are girly girls. And, well, Timmy Jr is still a dog, but that one's justified.

Real Life

 * As mentioned above, recently, it's been discovered that some acquired changes can be inherited, albeit in a weaker, less permanent, and (probably) less important form. The study of this is called epigenetics. Basically, chemical changes to the DNA can help inactivate or activate parts of it -- and because it's still DNA, these can be passed on. For instance, malnutrition might mean that your DNA doesn't methylate properly while you're growing up, and conditions in the womb can affect development of the fetus, which can pass on some information about the mother's environment -- how much food is available, and so on -- to the child. Science Marches On.
 * Experiments in rats have shown that cross-fostered pups of mothers who exhibit attentive parental care (licking and grooming behaviors, in particular) end up, through the action of acetylation and methylation, having less of an "anxious" response to stressors. When these rats become mothers themselves, they exhibit the same sort of parental behavior towards their pups, so it is a continuing cycle -- independent of genotype, the maternal attention is propagated to the next generation and so on.
 * Endosymbiosis is the current prevailing theory on the origin of certain organelles--mainly the mitochondria and chloroplasts--in the cells of eukaryotic (multicellular) life. The theory is that the organelles were originally entirely separate single celled organisms that were eaten by the eukaryotic cell but not digested properly. When the larger cell divided, so would the organelles, and so they were passed onto descendants without any genetic change.
 * Further, the organelles provide an energy source which was not previously available, so it could be argued that they cells were given superpowers by something that they ate, which was then passed on to their descendants.
 * Bacteria can pass down traits acquired through horizontal gene transfer. When two bacteria swap genes or "mate", the exchange is permanent and the altered genome carries on to all offspring.
 * In the late 1800s, there were several experiments to test Lamarck's theories, including one carried out in Germany that involved cutting off mice's tails to see if their children would be born with shorter, or no, tails.
 * As Isaac Asimov (or Carl Sagan?) has pointed out: Jewish boys have been circumcised for many generations, but still every Jewish boy is born with a foreskin.
 * Unless they are aposthic.
 * Some genetic diseases like Myotonic Dystrophy are subject to "Anticipation". This means that if one or the two parents show a slight variant of the disease, the children will not only inherit the disease, but often suffer a harsher and earlier form of it, and this will only increase with each new generation. The reason is that the disease is caused by having more than a determined number of repetitions of a certain gene sequence and since 1) everybody suffers mutations during its life (though they rarely have any effect or show up at all) and 2) repetitions are among the most common mutations, people with more repetitions are more likely to gain even more, and thus to pass a larger sequence to their descendants to begin with. It has been discovered recently that other diseases are also linked to repeated sequences (such as Fragile X Syndrome, Kennedy's Disease and Huntington's Chorea) and as result these might be subject to anticipation as well.
 * Anticipation is completely and utterly non-Lamarckian. The conditions subject to anticipation are congenital, although some of them (particularly Huntington's Disease) do only show up later in life, due to, for example, being caused by a gradual accumulation of a harmful protein (HD). When the reproductive cells divide (to make sperm or eggs), there is a high chance that the genetic code repeats which cause these conditions will expand due to the replication apparatus 'slipping' or 'stuttering' on the repetitive areas (it's more complex than that, of course, but most of the readers don't have genetics degrees). The reason these conditions can become worse down the generations is not due to any acquired factors from the parent's life, it's because there are problems with the creation of their gametes. Some conditions commonly showing anticipation effects are Huntington's Disease, Fragile X Syndrome and Myotonic Dystrophy.
 * Several percent of human genome is Endogenous retrovirus DNA. One of our ancestors got infected by a retrovirus, which made its way into the said ancestor's germ cells. Bingo! Now his/her children inherit the virus DNA with the parent DNA, until this day. Some of the endogenous retrovirus DNA has since mutated and became junk DNA sensu stricto, but some of those viruses are actually still active, for better or for worse (like helping the embryo implant in the womb, or playing a role in several diseases). It is highly unlikely the original infection was via a spider bite, though, or it would be a rare Lamarckian Funny Aneurysm Moment.
 * Cultural evolution does work like this, as ideas acquired in life (or mutations thereof) can be taught to one's offspring.
 * If your parents are 'intelligentsia' or 'politicians' or 'military middle class' you'll usually be expected to be good at the same sort of jobs, and be expected to grow up as one as well.
 * Before the development of trade schools and formal educations, most jobs were like this; boys were expected to grow up and take their fathers' jobs, especially more mundane positions, like farming, carpentry, and other manual labor jobs. If a boy wanted to learn a trade different from his father's, he would have to become an apprentice to someone else. It was simply easier to become an apprentice to your own father. Younger children might have had more options, though, because they weren't expected to inherit the family business.
 * Briefly thought to have occured with second-generation phocomelia, a congenital deformity primarily seen in infants whose mothers used thalidomide during pregnancy. Although the damage inflicted on these unborn children was environmental in origin, a small number of phocomeliacs subsequently grew up, married one another, and (rarely) produced phocomeliac children. Further investigation subverted this trope, revealing that children who'd been deformed by thalidomide had already been genetically predisposed to suffer such developmental flaws in response to chemical contaminants, and their second-generation children inherited a double dose of that susceptibility, making them subject to phocomelia even in the absence of thalidomide.
 * To a certain extent, this is true anyway, though less based upon what your parents did, and more what they needed to do to survive. For example, native-born Koreans don't sweat the same way, because not sweating is a way to survive in cold climates. Likewise tanning skin is likely an adaptation to very sunny climates. The process, however, is reversible over time if the need suddenly no longer exists.
 * Analysis of adopted Korean War orphans showed a surprising amount of genetic influence over the life of the child. The education level of the adopted parents had a puny effect on the adopted child's education (each year of maternal education translated to a four-week boost to the child) and the adopted parents had no effect at all on the child's adult income.