In The Butcher Bird, one of the Augment types created by CaptainGrigori Vinci is the Fae, which gives the person implanted with it the ability to turn into the form of anyone they have a DNA sample from.
In Fialleril's Star Wars fics, explored in most detail in the Double Agent Vader series, the Amavikka culture of Tatooine has legends about Ekkreth, a trickster who frees slaves and punctures the hubris of slaveowners. Ekkreth is a shapeshifter who takes the forms of harmless-looking slaves, or ignorant outworlders, or other people of various kinds (and can also be animals — a common ending to a story is for Ekkreth to turn into a bird and fly away laughing). Part of the message of the legends is that anyone you meet could be Ekkreth, and so could you.
The Flower Blooms Twice: Changelings, per canon. There's also a variant with Apple Bloom, who's revealed to have been an infant Changeling Queen discovered by the Apple family after Applejack returned from Manehatten (where she'd gone after her parents died). After finding her, Mac and Applejack decided to give her the ribbon once worn by their mother Apple Flower, and when it was tied into her mane as her signature hair bow, she turned into an exact replica of Apple Flower and has been in that form ever since, as long as she wears the bow, until events during the story that use up the magic within it. This effect's origin is later explained when General Coin reveals that ponies can leave an imprint, or Soma, of themselves in specific objects they've owned for a long time, and that changeling magic can interact with this imprint; this is why Apple Bloom turned into an infant copy of her ribbon's former owner. After the magic is used up, she has to learn how to change into her original form (or as close to it as she can) with her inherent powers.
Obake. A subcategory of Yōkai, supernatural creatures of Japanese Shinto myth. Obake are beings that can take on any shape, from an inanimate household object to the most ravenous of beasts. However, despite that, Obake can be of various species, possessing various base forms; cat, dog, monkey, even human are just some of them. Obake have generally lived in peace, respecting all those around them. Secluding themselves from people, they are one with nature, in perfect harmony with it and each other as they live through existences which aren't limited by the passing of time. Everything was perfect until that fateful day...
This is the primary power of the Changelings in Iron Kissed. While most Fae can use glamours to look like pretty much anything they want, few aside from Changelings can actually alter their physical forms.
Keepers of the Elements: The Erendorian people for the most part have this ability and some non-Erendorian people have this ability as well.
George displays a lot of new magical forms (other dragons, a centaur, elementals, a cockatrice, a cloud giant, a troll, etc.) and later reveals that he'd been reading the AD&D Monster Manual and gaming magazines while on Earth. He can also buff himself up.
Mike's New Ghostly Family: Liz Schmidt (formerly Elizabeth Afton) can shapeshift into a spectral form of Scrap Baby at will, making her the only ghost child capable of shapeshifting into an animatronic form. This form has stronger "physical" influence on the corporeal world, allowing her to break things more easily with her claw and hand. Initially, Liz hated this form, viewing it as a Mark of Shame on her soul, until her new father Mike Schmidt and her new siblings, as well as Michael Afton, who descended from Heaven to comfort her, were able to convince her to not view her new form as punishment, but to make Scrap Baby into what she wants her to be, as opposed to what William Afton wanted to turn her into, with Liz deciding to use the Scrap Baby form to become a protector of her new family.
The Moonstone Cup: The dragon queen Najstariot keeps herself in pony shape for the majority of the tournament with a transformation spell, since her true form is in the same size range as a good-sized town. It isn't until the climax of the story that she drops the transformation and shows Twilight her true, draconic form (and the injuries she's sustained in it).
My Family and Other Equestrians: According to the narration, it is possible that Lizzie's transformation may be voluntary, depending on how Discord pulled off the transformation and on whether Lizzie wants to change back.
Vampires in general are capable of turning into at least one of the following: bats, wolves, cats, toads, mist and rats.
Soma can turn into a bat because he Dominated the souls of Giant Bat and Bat Company. When he's temporarily turned into a vampire, he can do it without the souls and can also turn into a cat and mist.
Dracula could transform into mist, a wolf, a bat, and several other demonic forms.
Kazuya's pet Pascal can chose between his dog form and Cerberus form at will.
In The Parselmouth of Gryffindor, once he's gained sapience, the Boggart begins exercising to allow himself to take any shape he wishes instead of automatically transforming into a passerby's worst fear.
Past Sins: Nightmare Moon can reshape her form at will.
The Pieces Lie Where They Fell: Full Moon Sweet Surprise, a unicorn, is adept enough at transformation magic to fully change into different pony types. Likewise, Changelings and changeling hybrids like Page Turner have this as a natural ability, though Page admits at one point that she's not as skilled with it due to years of hiding in her unicorn form.
Serena is implied to have this, as her hair changes its natural color to black when she's sad about Ash's defeat in the Battle Dome tournament.
Another is Hilda, though in her case it's more of an illusory power, much like a Zorua/Zoroark.
Pittan from Pretty Cure Perfume Preppy, can turn from bird to human and back whenever he lets out a 'squawk'.
Realistic Pokémon: The series explains the illogical concept of Remoraid (a fish) evolving into Octillery (an octopus) by positing that larval Octillery simply mimics the appearance of actual Remoraids to seek protection from Mantines. Given the fact that there are real octopodes that employ similar tactics, this actually makes sense.
In the Virtual Series Slayer Academy two characters, Hamish and Rachel, have the ability to change their appearance. They can look like other people as well as changing all or part of themselves into various demons.
In NieR fanfic Tower of Babel Emil gains the power to shapeshift between his human form, Halua’s giant body, and their skeletal mix, each with their own pros and cons. And Amalgamates have the power to switch between Gestalt and Replicant form.
A werewolf in Weres Harry claimed that some of the ancient Scandinavians were given this ability by their gods — Loki for wolves, Tyr for bears and Heimdall for big cats.
George in With Strings Attached, thanks to his unexpectedly powerful ring. There don't seem to be any limits on what he can become or for how long, though he eschews certain forms because they're disgusting or disconcerting. But in the blink of an eye he can become animals, birds, insects, monsters (including a red dragon), other people, and even inanimate objects. Healing Factor, size shifting, and a Hammerspace “closet” are also part of the package, though Magic Pants are not. (He keeps clothes in his closet for that.) He does have a little problem with The Mind Is a Plaything of the Body, though with effort he can come back to himself. Also, his ring sticks once in a while.
OSMU: Fanfiction Friction: Nectar, one of Basil Valentine's henchwomen, has the ability to turn into a large black wolf and back again. It's implied that it has something to do with her not being human, just like Basil and his other henchwoman Ambrosia.
A Game of Cat and Cat: "(In)Effective Communication" has a mention of Soma being able to turn into a bat, since he was talking about weapon magic, and a Pun with the Batter Up! weapon was made.
Discord's New Business: The theme of the fic. Discord, for a fee, transforms his customer into what they want for 24 hours (or more).
The possible transformations are: Earth pony, pegasus, unicorn, alicorn, zebra, donkey, griffon, minotaur, old-type changeling (Pre-season 6), new-type changeling (Post-season 6), changeling royalty (Chrysalis and Thorax types), dragon, and draconequus. Special requests are possible.
Alicorn, changeling royalty, dragon, and draconequus are more expensive than the others, and require signing an "If I do bullshit during my transformation, it's my fault and not Discord's" form.
Later on, Diamond Dog, Genderswap, hippogriff, catfolk, tatzlpony, age manipulation and (for the reader's vote) transformation error are added to the list.
Some other forms are seen through other customers, like human.
has the protagonists changing into different Pokémon and Digimon in order to defeat their enemies, sometimes spending no more than a couple of seconds before transforming again.