Inspiration Nod

Sometimes a story isn't a remake, but borrows themes and/or situations from an earlier story. This isn't a Whole-Plot Reference or the Serial Numbers Filed Off, but rather the normal realm of artistic inspiration and literary allusions.

When one work is inspired by another, oftentimes its creators will slip in an affectionate Shout Out to the original as an Easter Egg. Nothing too overt--just a slight nod acknowledging the older work's influence on the newer one.

This Inspiration Nod will let people know that "Yes, we have seen the previous work" and "Yes, we do note the similarities between our works". It often appears in a very particular part of the production choices, something that would be outside of the natural course of inspiration but which unambiguously points to another work.

Say, you have the trench run in Star Wars and its connection to the The Dambusters. So George Lucas fills in a small detail, like the background chatter, with something from Dam Busters. It doesn't affect the actual trench run (compared to the targeting computer) but gives a little nod to the original inspiration.

Anime & Manga

 * Love Hina has taken some flack for lifting story ideas and plot developments from Maison Ikkoku. It is probably not a coincidence that Keitaro's aunt is named Haruka, the same as  from the end of Maison. This is further suggested by vocal casting Megumi Hayashibara as Haruka (casting an A-list star in a support role); Hayashibara actually debuted in in Maison (minor characters and background voices).
 * In Ray: the Animation... sort of... the story takes a lot of inspiration from Black Jack. In the manga, a character that is suspiciously similar to Black Jack shows up. The anime, though, just goes ahead and drops B.J. in there, because the studio that produced had the rights necessary to do so.

Comic Books

 * Writer Peter David called these his Pink Bunny Slippers after an example of one of his Incredible Hulk comic book storylines. He realised that there are parallels between between his Incredible Hulk story line and this other movie, Real Genius. There are similar plot points, so he makes a reference to it that doesn't involve using any more of the pre-existing connection but just throws in this shot of pink bunny slippers (as worn by both the University President and Val Kilmer in the movie) to lampshade it to anyone else who might have also spotted the similarites.
 * It is a bit of a Retcon, but Batman's origin (seeing his parents murdered) traditionally happened on the way back from seeing The Mark Of Zorro (an obvious inspiration for Batman himself).
 * Wolverine's "Old Man Logan" storyline draws many parallels to the movie Unforgiven. Likely why "Un-4-Given" is gratified on the side of the future Fantasticar in the first issue.
 * Alan Moore was either unaware of or had forgotten The Outer Limits episode,, when he was writing Watchmen. When someone pointed out the similarity it bore to , Moore and Gibbons had it playing on Sally's TV in one of the penultimate scenes.
 * Neil Gaiman's Sandman: The concept of taking a relatively obscure DC Universe figure and re-interpreting it with a deeper mythology was ground well-trod by Alan Moore, in his run on the Swamp Thing series. In his first couple of arcs, Gaiman throws in a ton of nods to Moore: the inclusion of the Moore-created John Constantine, the clues that Morpheus' pet Matthew is the reincarnation of the Swamp Thing character Matthew Cable, the similar plot of a formerly goofy DC universe villain taking hold of his powers to become a major threat that the Justice League can't handle, so the eponymous character must talk down (The Floronic Man/Doctor Destiny), and so forth.

Fan Fics

 * The Captain of the Virtual Console briefly mentions Captain N the Game Master and how it at least had a good premise.

Film -- Animated

 * The Incredibles has a family of four superheroes (plus a baby) with half of the same powers as the Fantastic Four. Naturally, the final villain (right after the origin story movie) is a subterranean conqueror, "The Underminer", who is a pretty close match to the Mole Man, the villain in FF #1.

Film -- Live Action

 * Demolition Man: Influenced by Aldous Huxley's Brave New World, Demolition Man draws its setting of peaceful, tightly controlled San Angeles of 2032 from the novel, and Sandra Bullock's character Lenina Huxley is named after the author and one of the book's characters as a reference.
 * The evil rich mastermind in Batman Returns is given the apparently Meaningful Name of Max Schreck (fright/scare). Actually, that was the name of the actor who played Count Orlock in the original Nosferatu. A way for director Tim Burton to tip his hat to the very 1920s German Expressionist look of his two Bat movies.
 * Throw Momma From the Train is built around the same let's-trade-murders plot as Alfred Hitchcock's Strangers On A Train. This is directly referenced in the movie, when writing teacher Larry tells his hapless student Owen to watch some Hitchcock for inspiration. Owen watches the first few minutes of Strangers, immediately recognizes the similarity to his current situation, and runs off to kill Larry's wife...
 * The Death Star attack in Star Wars: A New Hope owes a lot to the climactic attack in the movie The Dambusters, both in the way it was filmed and in the characters setting up a precise run to the target. This is made clear when much of the pilot chatter ("Say about twenty guns..." and so on) is lifted verbatim from the earlier movie.
 * Pandorum does this with Twelve Thirteen. Dennis Quaid even compares it to Star Wars.
 * Office Space had the main character and his friends robbing their company by rerouting the fractions of pennies that get rounded down when taxes are deducted. They comment that this is what Richard Pryor did in Superman III.

Literature

 * Stephen Fry's novel The Stars' Tennis Balls (aka Revenge) owes a lot to The Count of Monte Cristo. In acknowledgement of this, the major characters have names that are anagrams of or puns on the names of their equivalents in the earlier novel.
 * It's fairly obvious that the New Republic in Singularity Sky by Charles Stross is basically 19th century Prussia IN SPACE! Less obvious is that the Republic's military leader's delusion that he is pregnant with an elephant was shared by a real Prussian field marshal (Gebhard von Blucher) during the Napoleonic Wars.
 * In a few Sherlock Holmes stories, Edgar Allan Poe's C. Auguste Dupin (on whom Holmes is based) is mentioned; in one story Holmes explicitly does a trick that Dupin did in one of his stories: as they're walking along one evening, Holmes/Dupin responds to some unsaid thought that their walking companion had at the time.
 * Dickens Of The Mounted presents itself as the memoirs of Charles Dickens' Remittance Man son, but it's actually humorous historical fiction, which takes clear inspiration from the Flashman series, as is evident in similarly designed maps and a very similar Literary Agent Hypothesis claim by the actual author. In reference to the inspiration (and as a major "clue" the work is fictional), Flashman actually briefly appears in a Take That cameo, wherein he's presented as an Upperclass Twit suffering from various venereal diseases that would be the likely result of all of his womanizing.
 * Brutha, the protagonist of Small Gods is a beefy guy who has a Photographic Memory and becomes the prophet of a Crystal Dragon Jesus religion. These are traits shared with Severian, the protagonist of Book of the New Sun, and to this end, one character that Brutha encounters is named Severian. Incidentally, Small Gods is sort of an unofficial sequel or prequel to Pyramids, and in that book, one of the sections is titled "The Book of the New Son".

Live Action TV

 * Jessica Fletcher of Murder She Wrote seems to have been more than slightly inspired by Agatha Christie's Miss Marple, especially since series star Angela Lansbury had previously played Marple in the movie version of The Mirror Crack'd. The pilot of Murder She Wrote opens with a scene of the star little old lady solving the end of a movie mystery interrupted halfway, which is a direct lift from the opening of The Mirror Crack'd. Said scene is not in the book.
 * A case of internal borrowing: One Lazy Town episode echoes the plot of the play it was based on when Robbie Rotten in disguise takes over illegally as mayor. Although other than the 'taking over from the mayor' aspect the episode is very different, both play and episode briefly have the real mayor in a bunny suit for no good reason. Only hardcore or Icelandic fans would get it, though, as the play is both in Icelandic and very difficult for a non-Icelander to acquire legally. Also, many of the songs used in Lazy Town have the same tune (and general theme) as the songs used in the original plays.
 * Season 5 Episode 17 of Numb3rs contains a a number of references to the Robot series of Isaac Asimov, from which it borrows the plot device "an A.I. that kills a human." The episode's title is "First Law" after the Asimov's First Law of Robotics. The company in which the death takes place is called "Steel Cave Industries" after one novel in the series, The Caves of Steel. The name of the A.I. accused of murder is "Bailey" after the protagonist of that novel, Detective Lije Bailey. The scientist who is killed is named Daniel and gives his admin password as "Daniel Olivaw" after Lije Bailey's robot sidekick R. Daneel Olivaw. Presumably this scientist was the one responsible for naming the A.I. and the company created to fund its development, so his familiarity with these books gives an in-story explanation for all these references.
 * The Parks and Recreation episode "Pawnee Goddesses" has Leslie engaging in a battle of the sexes between her girlscout group and Ron's boyscout group. At one point, to impress Ron's group, Leslie's friend Ann shows that a large fish she caught, and then admits to the camera that she bought the fish from a grocery store, and got the idea from an I Love Lucy episode. This alludes to an episode called "Deep Sea Fishing" that also had a battle of the sexes plot, but might also be a nod to Leslie and Ann having a similar dynamic as Lucy and Ethel.

Radio

 * The Doctor Who Big Finish audio Master is fairly blatantly a take on The Strange Case of Dr. Jekyll and Mr. Hyde. Apart from direct references to "John Smith"'s copy of the novel, there's a more subtle nod with one of the characters having the maiden name Utterson.

Video Games

 * Slydris is a Tetris variant, and as a nod to its predecessor, it has three music tracks you can choose from, labeled A, B, and C.

Western Animation

 * An episode of the short-lived Clerks the Animated Series features a weird plot that devolves into a fight with the animator, who keeps painting Dante and Randall into weirder and weirder situations. The similarity to the Daffy Duck short Duck Amuck is shown through this trope by having Randall temporarily turn into the same flower-head creature that Daffy turned into.
 * In the Batman Beyond Fully-Absorbed Finale in Justice League, it's revealed that Terry McGinnis's family was supposed to have been killed after watching a film about the Grey Ghost, a superhero who happened to be an inspiration for the DCAU Batman in Batman: The Animated Series.