Goo-Goo Godlike

Or superpowered, godlike infants and very young children.

Apparently, Plot Leveling happens inside the fictional (and, especially, superheroic) world as well. Not only is it true that Lamarck Was Right about parents passing on their more noteworthy abilities through a number of increasing Evolutionary Levels (never mind that that last bit is there only if you read between the lines real hard), but more powerful people are born chronologically later; just ask anyone who's been to The Future. This trope is most pronounced in those who are currently infants: They don't get any lines or characterization, but they still alter the fate of the world just by existing.

Maybe it's all that Infant Immortality building up and exploding into the world as Pure Energy, or maybe it's just some writer's idea of a "surprising" development, but if you see a baby in any genre which lets people have power disproportionate to their physical and mental ability, that kid is going to be God.

Woe betide any babysitter (or parent) who cannot quite control the baby's immense powers.

Contrast Puberty Superpower, where your abilities show up later. Happens because of Superpowerful Genetics. Do this on an industrial scale and you get a Bizarre Baby Boom. When one of these goes wrong, it's an Enfante Terrible.

Anime & Manga

 * Dragon Ball:
 * Goku was sent to Earth because he'd easily be able to wipe out all life on the planet as a newborn baby. That's not speaking highly of Goku; that's speaking badly of Earth. We're so back-water and worthless we're not even worth a proper invasion, just send a baby there, let it full-moon-rampage for a few years, then send someone to clean up whatever's left over.
 * Any Saiyan Half Human Hybrid can be relied on to crush a Big Bad who has otherwise proved unstoppable. Two of the Big Bads of the series (Vegeta and Cell) are defeated by Gohan as a toddler and teenager respectively. However, it's also subverted in that these power spurts are the result of short-lived moments of Unstoppable Rage; Gohan didn't constantly train and focus to keep up his might or to hold his temper in check, and that's largely why Goku is the one to defeat Frieza and Majin Buu.
 * This grows worse as the series progresses, too: Goku and Vegeta had to go through great suffering to obtain Super Saiyan. Gohan merely had to imagine going through great suffering. Goten merely had to get scared sparring with his mother, and Trunks could do it because Goten did it. Vegeta lampshades this both in Japanese and English.
 * Ivan Whisky aka Cyborg 001 in Cyborg 009: he's just a little baby, but has insanely powerful psychic powers and is extremely intelligent.
 * While not at all godlike in any way, Hiei of Yu Yu Hakusho needed to be wrapped in a special cloth and sealed with many talismans because he was surrounded by an aura of fire that was especially hazardous to the ice demons around him.
 * Pokémon:
 * Brock's Happiny is an amusing case of "doesn't know her own strength". The father of the egg must have been a Granbull... This is of course, ignoring the fact that, at least in the games, Happiny has the lowest attack power of any Pokémon. That may well be intentional.
 * And, to a point, Togepi did in earlier seasons... sort of. Its Metronome was very convenient in many situations, even if none of the cast realized it. In the games, Metronome (which randomly uses almost any move in the game, except for whichever moves the Pokémon actually knows and a handful of other exceptions) is too unreliable to be useful. In the anime, though, whenever Togepi used Metronome, you could count on something impressive (and usually explosive) happening.
 * Vivio of Magical Girl Lyrical Nanoha, the title character's adopted 6-year-old daughter who . Looks like Nanoha has a worthy successor to the "White Devil" name. Being, explains pretty well why she's so powerful.
 * All of the naturally born Mu children from Toward the Terra, but especially Tony who, at the age of three, almost killed a man (deliberately!) with his Psychic Powers.
 * Akira from the eponymous manga is a child with extreme psychokinetic powers. He was so powerful that he had to be sealed away in an underground facility at below freezing temperatures.

Comics

 * Alexander Luthor Jr. made his debut as the ultimate MacGuffin in Crisis On Infinite Earths. And from there, he eventually went on to become the Dimension Lord Big Bad of Infinite Crisis.
 * Fantastic Four:
 * Franklin Richards, son of two members of the Fantastic Four, can do literally anything. Basically, Franklin has two separate superpower sets: he is explained as possessing both the cosmic radiation which empowered his parents and being a Mutant. Mutants usually acquire their powers during puberty (with physical mutations, such as Nightcrawler's physicality, happening sooner), but his are unlocked faster because he inherited power from his parents.
 * His little sister Valeria aka Val has genius-like intellect... and is not older than five. (Notably, genius adult intellect, as a five-year old with a genius IQ might have the intelligence of, say, a nine-year old.)
 * X-Men:
 * Nathan Christopher Summers of the X-Men is an amusing twist: he generally appears as the time-travelling adult Cable, in which persona he is among the mightiest mutants in the world... but the present-time infant version has shown bursts of even greater power, thanks to Apocalypse being pissy and giving Nathan a techno-organic virus. However Nathan Grey of Age of Apocalypse was never infected and was shown to be much stronger than his biologically identical counterpart from another mother. The Summers' Tangled Family Tree is so much fun.
 * Cable's evil clone Stryfe was originally far more powerful as well (since he too lacks the techno-organic virus), but not to the extreme levels that Nate Grey reached. Cable's power has greatly increased since the last time he fought Stryfe, so they're probably on more even terms now.
 * Gabriel Summers a.k.a. Vulcan, Cyclops's long-foreshadowed second brother. He was found as a baby and raised to adolescence by aliens, and has the power to absorb literally any form of matter or energy and fire it back, survive in the vacuum of space, and shut off superpowers. He was described as "beyond Omega-level", but since Omega-level already means a mutant of unlimited potential, the part about being beyond a mutant of unlimited potential is most likely a regretful mistake. Still, he's very powerful.
 * A further Marvel Universe example was Hyperstorm, the alternate future child of two of these, Franklin Richards and Rachel Summers. His powers include controlling the fundamental forces of the universe, moving to any point in the universe instantly through hyperspace, and ridiculous levels of psychic power. (He was still vulnerable to being eaten by Galactus, though.) This isn't terribly surprising with a dad who can re-arrange reality and a mum who is so powerful a telekinetic she can create a black hole and then destroy it just as easily, and that doesn't even start on all of her other abilities.
 * In the WildStorm universe (home of The Authority, Planetary, and more), several superpowered "century babies" were born in the year 1900. Jenny Sparks, seemingly the most powerful of these, was actually the embodiment of the 20th century, and died shortly after it ended. Thus far, only a single century baby is known to have been born in the year 2000: Jenny Quantum, Sparks' godlike spiritual successor and quite possibly the most powerful being in the WildStorm universe. She's even singlehandedly, effortlessly defeated Lobo.
 * The Blake twins in Spawn are not godlike:  Cyan had also some power over Spawn during her baby years, but now, as a preteen, she has become more of a protegé.
 * Sometimes this applies to even Normals. X-Men has the powerless Dr. Moira MacTaggart, whose status as Professor Xavier's ex-girlfriend was enough to knock her son, Kevin aka Proteus, into Green Lantern Ring power levels.
 * Superman:
 * Superman was originally one of these as a child; these days he's usually portrayed as having Puberty Superpowers. The often unintentionally unsettling "Superbaby" comics and cartoons are a good demonstration of why so many comics try to avoid all this. Kyle Baker did a story called [[http://en.wikipedia.org/wiki/Letitia_Lerner
 * Ariella Kent, the daughter of an Alternate Universe Superman and Supergirl (they're not cousins in that world) has greater-than-Silver Age Kryptonian powers, plus an array of Psychic Powers and Time Travel. She causes massive collateral damage every time she... well, does anything.
 * In JLA Act of God, the child of the depowered Supes and Wonder Woman is shown using telekinesis.
 * Black Bolt of The Inhumans nearly destroyed his home just by crying as a child.
 * born in S.H.I.E.L.D #4.
 * The Star Child, son of Ken Connell, in The New Universe. Born with the Star Brand already within him (Ken had sex with the child's mother while in possession of the Brand), he's actually pretty damn power, going so far as to stop death itself from happening. He later fuses with Ken and, takes blame for the White Event and Black Event, then bolts.

Films -- Animation

 * Baby Jack-Jack of The Incredibles, for a reveal. The short Jack-Jack Attack rather hilariously deconstructs the implications of godlike babies for those who have to look after them. Observe.
 * Disney's Hercules opens with several scenes of this.

Films -- Live-Action

 * In the film Day Watch, Yegor is a super-powerful Dark One able to lead the dark ones (or light ones) to victory over the never ending struggle between the two forces. Naturally he's a small boy who's just about to enter pubescence. He's a lot younger in the first film Night Watch
 * In the climax of 2001: A Space Odyssey, David Bowman's final, god-like form is the "Star Child", which mostly resembles a human baby.

Live-Action TV

 * Charmed:
 * Piper's son will be the ultimate agent of either good or evil. This is mostly due to the fact that he's a son of both a White-lighter and a Charmed One.
 * Phoebe's son was also destined to be an ultimate agent of either good or evil, since it was the child of a The Source and a Charmed One.
 * Ghost Whisperer: Melinda's future child will have more/different powers over spirits then his mother; just what those powers are haven't been revealed yet, but it's enough to disturb the spirit world into haunting Mel with faceless children and books of doom.
 * Isabelle from The 4400 is extremely powerful as an adult in series three and four, but back in series two she was just a baby, and still powerful enough to terrify her own father. When her family is being pursued by rednecks, the infant Isabelle mentally forces them to kill each other. She was even powerful enough to temporarily incapacitate Jordan Collier while still in the womb.
 * The Genius Ditz superhero Thermoman in British sitcom My Hero had a son, Ollie, who was just as powerful as his father - but also twice as intelligent.

Literature

 * In Robin McKinley's Spindle's End (an expansion of the various "Sleeping Beauty" stories) magic permeates everything and the "Fairies" are actually normal people who happen to have the inborn ability to control it. The Fairy condition may not necessarily be hereditary and most Fairies come into their power as teens. However, a few Fairies manifest powers very early, a phenomenon known in the novel as "Baby Magic". As cutesy as that sounds, it's actually very dangerous and unpredictable, especially because yu never know how those powers will manifest. A baby Fairy may be able to intuitively understand Animal Talk. Or, he may be able to transform the nanny into a terrier and pull a One Winged Angel act every time he has a tantrum....
 * Coin the Sourcerer from Discworld. Shortly after being born he get hit by lightning and merely absorbs its power. By the time he's a teenager he's the most powerful force in the world.
 * Two years after Coin from Sourcery, Terry Prachett co-wrote Good Omens with Adam the 11 year old Anti Christ, who shares quite a few traits with Coin.
 * Surprise Golem from Xanth appears to be one of those initially, but turns out to have a significant handicap later on (though the handicap is less significant than it initially seems). Melody, Harmony, and Rhythm are legitimate examples.
 * It's a GOOD Life by Jerome Bixby. This kid's a Reality Warper, he can use People Puppets, he has Telepathy... and he's an instant generator of horror.
 * Charlie McGee, the eponymous incredibly powerful pyrokinetic of Stephen King's Firestarter.
 * Anton and Sveta's daughter in Twilight Watch.
 * Eriond from the Belgariad and Mallorean.

Myths & Religion

 * The son of the Norse god Thor was, of course, far stronger than any of the older gods.
 * Greek Mythology:
 * Hercules. His first heroic act was before he was a month old, when he killed two serpents created by Hera to take out him (and his normal twin) with his bare hands. This was discovered by his parents when baby Herc was found using the dead snakes as rattles.
 * Prometheus warned Zeus against this: Prometheus told him that a certain nymph named Thetis would bear a son who would be more powerful than his father. So they married her off to a mortal hero, the myrmidon King Peleus, and her son was "merely"... Achilles.
 * Hermes, according to the Homeric Hymn dedicated to him, was one day old when he walked across the countryside, stole a herd of cattle from the god Apollo, drove them back to his mother's cave while cleverly covering their tracks, sacrificed and burned one or two of them, and invented the lyre. Apollo was not amused, and chased Hermes all the way up to Olympus. Hermes then talked his way out of punishment.

Video Games

 * Kirby. The little pink Eldritch Abomination slayer with a bottomless stomach is specifically said in the anime based on the games to be a baby, and he acts like one.
 * Wynaut from Pokémon Ruby and Sapphire. Most baby Pokémon are useless but cute Joke Characters. But through a simple exploitation of its extremely limited moveset, Wynaut becomes a Lethal Joke Character capable of taking down the most powerful mons in the game, include the actual Gods. It had been put in the "Uber" tier, a banlist from normal competitive gaming, although the ban was at least partly because it can cause an infinite stand-off with another Wynaut.
 * Handwaved in Golden Sun: The Lost Age, it's stated that Eoleo got the same Psynergy Stone exposure that a few others got in the course of the first game. Additionally, he's on par with everybody else in Dark Dawn, so maybe Adept kids are just a handful like that.

Web Comics

 * This is the entire premise of Minus, a webcomic about an omnipotent little girl. The title character has created and destroyed entire worlds while playing. Frequently involves disturbing Fridge Logic / Fridge Brilliance which proves that even a sweet-tempered, happy little kid like Minus can do some mind-warpingly horrible things when given godlike power. One of the last things she does on earth is killing 'em all. That's not as bad as it sounds, though.

Web Original

 * My Son Zack is a short film that explores this trope from the point of view of the godlike child's (understandably deeply stressed) parent. And it is one heck of a Tear Jerker...

Western Animation

 * The Fairly Odd Parents:
 * Wanda and Cosmo's Baby Poof is "the most powerful baby in the universe". His father Cosmo also was very powerful as a baby, and he was why Jorgen outlawed fairy babies in the first place.
 * Foop. He gains godhood, drains the power of 2 planets, defeats Jorgan Von Strangle, sends a plague on Dimsdale, and changes said planets within an hour of his life, EFFORTLESSLY, with nothing but a bottle. His only weakness is his mindset of a newborn and weaknesses of one.
 * One Pinky and The Brain episode had the duo discover the baby Kal-El before the Kents. Although Brain initially wants to turn the kid into a Tyke Bomb after seeing his amazing powers, he eventually realizes he's not cut out to raise a kid, let alone one with superpowers. Pinky and the Brain return Kal-El to his ship, right before the Kents arrive.
 * The Legend of Korra, the sequel to Avatar: The Last Airbender, has Korra, the new Avatar. She first displayed bending skills in three of the four elements at the age of five.
 * In the My Little Pony Friendship Is Magic episode "Baby Cakes", Pinkie Pie is excited to have the chance to babysit the twins Pound and Pumpkin Cake. However, not only does she discover she's ill-equipped to actually take care of them, but Pound is a pegasus that can fly, walk on the ceiling, and physically demolish any attempt Pinkie makes to keep the twins restrained, while Pumpkin is a unicorn with all the requisite magical powers, including levitation and phase shifting.
 * Baby Smurf is enchanted and often demonstrates magic powers when a Deus Ex Machina is required without the other Smurfs knowledge with the lone exception of Papa.

Real Life

 * The concept of "indigo children", developed in The Seventies within New Age circles and popularized in the late '90s, claims that some children now are being born with special, unusual and/or supernatural traits. At least one variation of the idea claims that these children are the next stage in human evolution.