Fable Remake

A widely-known story is retold using the characters of the series in place of the characters of the original story. The original story can be from any number of sources: fable, play, short story, classic movie, historical events, etc. Christmas tales are often a favorite.

When it's just The Theme Park Version of a fable setting, it's likely a Storybook Episode.

Some commonly used are:
 * The Odyssey
 * A Christmas Carol (Yet Another Christmas Carol)
 * The Gift of the Magi ("Gift of the Magi" Plot)
 * Romeo and Juliet (Star-Crossed Lovers meets Feuding Families)
 * Star Wars (May the Farce Be with You)
 * "The Most Dangerous Game" (Hunting the Most Dangerous Game)
 * Its a Wonderful Life (It's a Wonderful Plot)
 * Alice in Wonderland
 * Freaky Friday (Freaky Friday Flip)
 * The Wizard of Oz (Off to See the Wizard)

Anime and Manga

 * Love Hina had an episode based on the Chinese tale of Son Goku, the Monkey King.
 * Whereas the entire Dragon Ball universe is also an adaptation of the story of Son Goku, the Monkey King. One guess which character represents Son Goku.
 * Yamcha?
 * The Forbidden Kingdom is either a remake of the tale of Son Goku, or its "prequel".
 * One of the manga chapters was based on the tale of Taro Urashima. Guess who got to be Urashima.
 * Yamcha?
 * Ouran High School Host Club had a manga chapter based on Alice in Wonderland, and a considerably looser adaptation in one episode of the anime.
 * In Yu Yu Hakusho, the gang fights a team of baddies who are perversions of the main characters from various Japanese myths.
 * Hello Kitty once did "The Little Match Girl". Yes, with the original ending.
 * There's an entire series of Hello Kitty and her friends performing fractured fairy tales called Hello Kitty's Furry Tale Theater.
 * There's a series of manga illustrated stories that transform a lot of the Grimms' more famous works into yuri, and twist the ending. For example, "Snow White" ended with the eponymous character living with the seven woman and "The Little Mermaid" ended with the protagonist falling in love with her sister since the princess was a flirt who didn't notice her.
 * Monster broadly mimics the story of the Beast from Revelation 13, but there are many subplots which mirror many popular fairy tales, including "Beauty and The Beast," "Hansel and Gretel", and "The Pied Piper of Hamelin." There is also an in-universe example, in that the characters unwittingly enact the plots of Bonaparta's fairy tales and his son's puppet show.
 * One chapter of Yandere Kanojo retells "Cinderella".

Comic Books

 * X-Men Fairy Tales is a series of these, casting the X-Men in the role of characters from various fables.
 * Followed up by Spider-Man Fairy Tales and Avengers Fairy Tales.
 * Sometimes in The Spirit Will Eisner would create new versions of fairy tales, set in the 1940s.

Fanfic

 * A Fan Fiction story called "The Wizard of Obligatory" is a cynical parody of the idea that puts Baldur's Gate characters in Oz for no reason.
 * The Doctor Who fanfic setting This Time Round has enough of these that they have their own section, "Story Time!".
 * An old Slayers fan comic posted on the Internet featured the cast putting on a production of Hamlet, with such gems of casting as Zelgadis as Hamlet and Prince Phil as Polonius. Hilarity Ensues.

Live Action Television

 * The third episode of the 1980s Degrassi Junior High is based on the story of the Emperor's New Clothes. The resident High School Hustler sells "hallucinogens" (actually vitamin pills) at five bucks a pop. Because nobody wants to admit they aren't "cool," his clients pretend to trip and even go through placebo highs.
 * Futurama and That 70s Show have both done dream sequences based on The Wizard of Oz.
 * It doesn't get a whole episode, but the 200th episode of Stargate SG-1 includes a scene in which Vala retells the story of The Wizard of Oz starring herself and the other members of SG-1.
 * The original Outer Limits did "haircuts" (as the production team called them) of "Beauty and The Beast" ("The Man Who Was Never Born") and Macbeth ("The Bellero Shield"). Coincidentally,, both episodes starred Martin Landau.
 * The Doctor Who 2010 Christmas Special was based on A Christmas Carol (the Doctor deliberately invokes the story in an attempt to change someone's life).
 * The whole premise of Grimm; set in contemporary Portland, OR, the main character is a police detective who is also the last living descendant of Jakob & Wilhelm Grimm, who in turn were part of a group of people who had the power to see supernatural creatures that appeared human to those without such an ability. The creatures were the inspiration for several fairy tales an folk takes around the world, Grimm or otherwise. Most episodes at least partially reference the original story.

Web Comics

 * To cap off 2008, Girl Genius did a Mad Science mockery of Cinderella - complete with Pumpkin Blimp and twist ending.

Western Animation

 * The Simpsons has done a few episodes like this. The original "Treehouse of Horror" featured a sequence based on Edgar Allan Poe's "The Raven", with Homer as the narrator and Bart as the titular bird. This was later done in "Simpsons Bible Stories", "Simpsons Tall Tales", "Tales from the Public Domain", and "Simpsons Christmas Stories".
 * Futurama. In one of the 'Anthology of Interest' episodes, Leela has a dream which retells 'The Wizard of Oz', with Leela as Dorothy. It turns out it was All Just a Dream and And You Were There insues.
 * They also parodied this one time by having the family complaing about how often TV shows retell "A Christmas Carol", and then showing Star Trek meets.. well you know.
 * Garfield and Friends was very fond of these, especially in its US Acres sequences.
 * Was the whole point of Alf Tales, a Spin-Off of the Animated Adaptation of ALF.
 * Rugrats has an episode where Tommy's maternal grandfather tells them the story of Passover, which the babies imagine themselves in, while a later episode did the same with the story of Hanukkah. Another episode involves a Suzie dreaming she is Dorothy from the Lizard Wizard of Oz
 * The Family Guy special "Blue Harvest" has Peter re-telling the story of Star Wars with himself as Han Solo and all the other characters as various faces through the galaxy far, far away. It was eventually followed up by retellings of The Empire Strikes Back ("Something Something Something Darkside") and Return of the Jedi ("It's a Trap!").
 * The 2003 version of Strawberry Shortcake has retold Cinderella, Sleeping Beauty and Rapunzel. The retelling of Rapunzel is basically In Name Only, as the titular character is already a princess, but so wild and free-spirited that her tutor places her in a tower to keep her from being distracted from her lessons in being proper royalty (super-long hair is apparently very regal).
 * Jim Henson's Muppet Babies often had the kids imagining themselves as the characters in various well-known stories.
 * Done in the Adventures from the Book of Virtues episode "Courage" (1998), when Aristotle the prairie dog tells Zach the story of "Zach and the Beanstalk", in which Zach plays the character of Jack.

Video Games

 * Enslaved: Odyssey to the West is a remake of Journey to the West.