There are many characters whose ability to transform into animals is a special power. Several of these are Shapeshifters whose power is limited to animal forms, and oftentimes a set number at that. There are also quite a lot of Shapeshifting characters who can turn into anything, but prefer to transform into animals, presumably because you can get more done in the shape of a living being than something inanimate. Our Werebeasts Are Different covers werebeasts.
Others are characters unwillingly transformed into animals, usually as a punishment (ironic or otherwise) or curse, more often than not by the dark magic of the Big Bad. In any case, regardless of species, the target is none too happy about being an animal. (Indeed, for some reason, characters are often just as upset over being turned into swans as they would be if they were turned into worms. There is an intriguing amount of Cursed with Awesome associated with this trope.) The target may lose the ability to speak, and must work hard to get the message to their friends about what happened. This is sometimes combined with a "Freaky Friday" Flip, leaving the animal's mind trapped in the human character's body (where Hilarity Ensues). This is frequently accompanied with some sort of time limit, after which it will be difficult or impossible to reverse the process.
Ichigo of Tokyo Mew Mew is a borderline case. The intended effect of her cat genes is the ability to voluntarily transform into a Cat Girl; however, as her cat DNA starts to overtake her human DNA, she starts involuntarily growing cat ears and tail when excited, and eventually begins to fully transform into a cat. Another recurring character in the show can become a cat voluntarily, but only for a limited time.
Yoruichi in Bleach spends a lot of the series as a cat because she likes to. Most of her transformations to and from human are to mess with other members of the cast (like Ichigo).
One Piece has the Zoan variety of Devil fruits, which allow the eaters to transform into a certain animal depending on what the fruit is, as well as a half-human hybrid of said animal (and yes, even humans are counted as an "animal"). Most fruits have a certain "model" for animals that are in the same family (EX: Dog Dog fruit, Model Wolf), or different sub-branches like "Awakened" which is more beast then man, "Mythical" like a Phoenix, and "Ancient" like a T-Rex.
Even inanimate objects can "eat" a Zoan Devil Fruit: they gain characteristics of a living being and their corresponding animal's intelligence, and can also transform into the animal itself, a hybrid (in the absence of a better word) or their "original" object form.
If an animal eats a Zoan fruit corresponding to its own species it becomes enlightened.
In Ruin Explorers, Ihrie was cursed as a child so that she turns into a mouse whenever she casts magic. Fortunately, she carries along a medicine that can reverse the effects, though having a limited supply at any one time means she still has to choose her battles.
Pokémon has an episode in the Johto League saga wherein Ash meets a witch named Lily. She has a recipe for a potion that will let you read a Pokemon's mind, but needs some ingredients first. At the end of the ep, Ash is turned into a Pikachu, which is affectionately nicknamed Ashachu. It launched a hundred Fan Fic sequels when that happened.
Snowbird from Alpha Flight is an Inuit demi-goddess who can shift into any animal, but it's always an albino female. For a time, she could only shift into creatures native to Canada (for that matter, she couldn't leave the country's borders without dying). Those restrictions faded with her immortality when she lost her virginity, but she still uses Arctic creatures as a preferred style.
Changeling—formerly Beast Boy—from Teen Titans. Like his cartoon counterpart, he can turn into a green version of any animal (though he can't turn into larger animals without strain). But unlike the show, he can speak in any form. This is because he's not limited to turning into animals, it's just his style.
Viktor Romanov in Nikolai Dante can turn into a giant eagle due to his weapon crest.
Daine in Tamora Pierce's Immortals quartet is a shapeshifter thanks to her Wild Magic. She has increasing control over her transformations as the books go on, though she retains her human mind even within the animal shape.
Several characters in the Harry Potter series (such as Professor McGonagall and Sirius Black) are "animagi", who can transform into specific animals (McGonagall becomes a cat, Black a large dog). Unlike most instances, this practice is very strictly watched by the government (who keeps tallies on the number), and is said to be incredibly hard to do.
Wizards in Ursula K. Le Guin's Earthsea books are capable of transforming into animals, though the process is dangerous. In one particularly memorable example, the protagonist Ged turns into a hawk in order to escape an enemy - and, forced to spend weeks in his new form, almost ends up getting stuck that way.
absolutely hilarious when you think about the fact that Ged is played by Shawn Ashmore in the SyFy version of the first book, that Ashmore was Jake Berenson in the TV version of Animorphs, that Jake saves Tobias from a swirly before the first book... and that Tobias ends up stuck as a hawk (red-tailed hawk, to be exact) at the end of the first book.
Wizards in Nightrunner can turn themselves and others into an animal form that is said to be their "true nature." The fact that it can be done to others, of course, means it's not always voluntary.
Many of the evil characters in The Caretaker Trilogy are Half Human Hybrids of some sort, but the only one shown to actually be capable of turning into the animal whose traits he borrows is Colonel Aranha. For those who didn't get the Meaningful Portuguese Name, he turns into a gigantic tarantula.
In the Xanth series, Dolph can turn into any living thing as his magical talent, while his grandfather Trent can turn any living thing into another living thing as his.
Dinah and Dorinda, the main characters of Eric Linklater's children's novels The Wind on the Moon, use a magic potion given to Dinah by a witch in order to transform themselves into kangaroos. They are, however, stuck in kangaroo form until they can locate the bottle with the potion to transform them back to humans, which leads to them being caught and put in a zoo. In the zoo, they also meet Mr. Parker, formerly a human detective, who was transformed into a giraffe for no apparent reason (he blames it on wishing he was taller back when he was human).
In the Chronicles of the Cheysuli series, the eponymous Cheysuli can turn into the shape of their Lir (a Bond Creature that is some kind of animal bear, wolf, hawk...) some can turn into the form of any Lir they want.
In Rick Riordan's The Heroes of Olympus series Frank Zhang a demigod son of Mars can be anything. According to Mars this means anything within reason, any living animal. This gift did not come from Mars however, but Poseidon, who is a distant ancestor on Frank's mother's side. His whole family can do it, and have for generations going back to Periclymenus a legendary Greek hero who Poseidon first bestows this gift on. Percy, Poseidon's actual son, is noticeably jealous of Frank's gift.
Hoole in Galaxy of Fear is of a shapeshifting species but, while Shi'ido are able to turn into anything at will, he only ever takes the shapes of different sentient species - Wookiees are a favorite - or animals, rather than ever staying with his default form and lengthening his arms, say. Though he is able to speak Basic while Wookiee-shaped, which real Wookiees can't do.
Manimal has a main character with transformation into animals as a special ability.
In True Blood there is a shapeshifter community. They can turn into any animal they want; they just have to see it in order to "copy" it. There is however an exception: each person has an animal that they feel comfortable with, and can transform into it at any time without having to see a real example. The ability is passed from generation to generation.
The TV Miniseries version of Earthsea had a story about a wizard who got so obsessed with shapeshifting into a bear that the bear's personality eventually displaced his own, causing him to eat his entire family. The story comes from the first Earthsea novel, "A Wizard of Earthsea", where the bear-wizard is only said to have killed his son.
Myth Quest has the protagonists going into multiple myths. Naturally, this happens.
Loki turns himself into a bird in "Hammer of the Gods"
In "Red Wolf's Daughter", the spirits of Eagle, Badger, and White Buffalo are summoned. All take human form.
Done in the "Metamorphosis" illusion from Theatre of Magic, where the magician turns into various animals, such as a dove, a tiger, or a cobra.
The New World of Darkness sourcebook Skinchangers has options for playable characters using almost every possible variation of this trope, with War Against The Pure and Changing Breeds adding a few more for good measure.
Almost every type of supernatural creature in the New World of Darkness is capable of shapeshifting into an animal by one means or another.
Werewolf: The Apocalypse is obviously about werewolves, but also lets you play as were- hyenas, spiders, cats (lions, tigers, leopards, lynxes, etc.), ravens, bears, foxes, crocodiles/alligators/lizards, snakes, coyotes, rats, and sharks. Extinct races include the werebats, wereaurochs, and wereboars (though even they have rules for playing them).
Vampire: The Masquerade has three clans with specialized disciplines that allow for animal shapeshifting: the Gangrel have Protean (the typical bats, wolves, and fog, though variations exist); the Followers of Set have Serpentis (guess); and the African bloodline Akunanse have Obomwe, which allows the Kindred to turn into any animal provided she smears her body with its blood (the creature must obviously be big enough to have enough blood for this to be possible).
Changeling The Dreaming has the pooka, selkies, commoner hsien, and inuas (a Native American kith). A member of these kiths has one animal form that she can shift into. The pooka and inuas choose one at character creation, while the selkies turn into seals, and each commoner hsien kith has one animal form its members shift into: cats, fish, monkeys, snakes, and badgers (in case you're curious, the noble hsien kiths are based on the 5 Taoist elements)
In Exalted, the Lunar Exalted are able to take the form of any species, so long as they've drunk the heart's blood of a member of that species, and can build up an impressive library of forms this way. They can also apply this to humans, although it works a little differently (each human form they add to their library allows them to take that /specific/ human form).
It actually works that way for animals too. You are taking that animal's form. It's just that the most common hunt is for one that's an excellent specimen but doesn't stand out. You could, say, hunt an espionage target's favorite dog so you'd be close to him for an extended period.
The Dungeons & Dragons Barbarian-based PrCBear Warrior is able to transform into a type of bear while they rage.
And druids can turn into any animal.
Wizards too, with the right kind of spells. And (like druids) transform others into harmless critters as per the second example of this trope.
In New Horizon, Medeans merge with the genetic code of the native wildlife. Unlike most other examples of this trope, this is PERMANENT... although, oddly, it doesn't effect any kids they have.
Tha Makuta in BIONICLE liked to take on animal forms, most famously Miserix, who preferred reptile forms to his original body (his only existing official image also has him turned into a dragon). The Phantoka Makuta team chose the form of bats, while the Mistika team took on the semblance of insects. However as a subversion, due to a mutagen, they couldn't turn back.
Druids in Warcraft III could turn into the totem animal whose demigod they were devoted to.
Druids in World of Warcraft can turn into various animal shapes. Bear, Cat, Seal, Bird, Tree and an owlbear thing.
Dragons are also known to have a human form, notable ones being Kalecgos, Alexstraza, and Neltharion (Deathwing as most players know him).
It's not ALWAYS human. Alextraza and her consert turn into High Elves, Chronomaru turns into a Gnome, Ysera becomes a Night Elf. Goblin and Blood Elf forms have been seen as well for other dragons. Also Deathwing human forms or his human one has changed a lot since his days as Lord Prestor.
Deathwing's human Form retains the reforged lower jaw that he has in his dragon form. (See Fridge Horror.)
Most Dragons in Fire Emblem games can transform from one form to the other, with varying degrees of ease. There are a few unique cases because the games all take place in different universes.
Fire Emblem for the GBA seems to imply that it's quite difficult for dragons to switch from form to form without losing their memories and personalities from their other forms.
Sword of Seals and Sacred Stones both required that your Dragon unit have a stone with a limited number of charges in their possession in order to switch forms.
Path of Radiance and Radiant Dawn added the Laguz, of which Dragons were one of the many races, who could transform from one form to the other at will, though they would revert to their humanoid state when they ran out of transformation points. A select few characters could stay transformed as long as they willed it, but most of them had their stats cut to make up for it. In Path of Radiance, the Laguz would transform without the player's choice or input when their meters were full, but Radiant Dawn allowed the player to activate it whenever they wanted so long as they had transformation points to use.
Fire Emblem Awakening decides not only to return the Manakete system, but also create the Taguel, a weird hybrid of both Manakete and Laguz mechanics that use magic stones to turn into giant rabbits.
In the Banjo-Kazooie series, visiting one of two shaman-type characters (Mumbo-Jumbo in the original and Grunty's Revenge or Humba-Wumba in Tooie) would allow you transform into different things; this is usually an animal (but not always; other transformations have included a tank, a submarine, and a washing machine). Oddly, the main characters are already animals.
The entire premise of the Bloody Roar game series is based on this trope.
In The Legend of Zelda: Twilight Princess, Link transforms into a wolf. It is initially involuntary due to the Twilight invading Hyrule, then Zant curses Link to make it permanent; eventually, the Master Sword breaks the curse, and Link gains the ability to transform at will. Interestingly, instead of throwing away the gem that cursed Link in the first place, they hold onto it, and apply and remove it using the Master Sword to switch forms.
In The Legend of Zelda: A Link to the Past, entering the Dark World without the protection of the Moon Pearl causes Link to transform into an adorable, defenseless, pink bunny-man. All in all, becoming a wolf was a much better deal.
Solatorobo provides a rare inversion: In a world populated by anthropomorphic dogs and cats, the main character can transform into a human to become more powerful.
In Kingdom Hearts II, one of the visitable worlds is the Pride Lands. While there, Sora is transformed into a brown lion cub thanks to his clothes. Goofy and Donald are also transformed into, respectively, a tortoise and a bird... that can actually fly.
On gaining the Transformation Staff, characters in Final Fantasy: The 4 Heroes of Light can turn to and from animals at will (which becomes helpful and sometimes necessary because of Animal Talk). Aire is a cat, Yunita a rabbit, Brandt a dog, and Jusqua... a chicken.
Ellen once turned herself into a duplicate of the family cat, "Brownie". She could still talk via magic and retained her mind.
In Zoophobia, shapeshifters can change into different animals. Avians into birds, serpentines into snakes and so on.
Kodotai, Bestiario, Manimal, and Menagerie from the ''Global Guardians PBEM Universe all have the power to assume the shape of any animal species they want. Russian hero Ursa can turn into a giant brown bear. Indian hero Bagha can turn into a large Bengal tiger.
In the Whateley Universe, Feral has the power to change into pretty much any predator mammal. There are also Weres who can shift into animal or were-animal forms, plus some mutant Shifters can do it. (Some mutants end up stuck in the involuntary version because of the way their power first manifests.)
Dragore from both Furtopia RPs of Darwin's Soldiers was turned into a dragon for unspecified reasons.
Professor Sehack from the rebooted Furtopia RP was turned into a Bengal tiger for unspecified reasons.
Beast Boy from Teen Titans has this as a special power. Interestingly, the involuntary subtrope occurs in the episode "Bunny Raven, Or How to Make a Titanimal Disappear". Mumbo the Magician changes the Titans into various animals. Beast Boy is rendered only able to change into inanimate objects, with a lamp as his base form.
In Young Justice, Beast Boy also has this ability, presumably due to the blood transfusion from the shape-shifting Miss Martian. Though he can take any animals’ form, he goes with various primates most often, because they are his favourite animals. Since he was bitten by a monkey shortly after said blood transfusion, his default form is that of a green, stooped, tailed half-monkey boy.
Jayna of the Wonder Twins from Superfriends. When the twins touched, Zan could turn into some form of water/ice, while Jayna could transform into any sort of animal.
The Monkey Talisman in Jackie Chan Adventures. The owner can turn him/herself or others into any animal they can think of.
Wild Kratts has this as the founding concept, in which the main characters can assume animal shapes using the Applied Phlebotinum in order to get close to the real animals.
In the first episode of the original Teenage Mutant Ninja Turtles, Bebop and Rocksteady volunteer to let Shredder turn them into a warthog and rhino, respectively, to get revenge on the turtles for humiliating them.
In Fullmetal Alchemist, it's possible to combine human beings with animals to create chimeras. If the procedure comes out right, the creature should have human intelligence and several traits from the animal they're mixed with (both advantageous and drawbacks), and some can even shift from their half-animal form to an apparently normal human. They are kept a secret from the public because of the obvious ethical issues they pose (lets just say the subjects did not volunteer for the experiments). So far we have seen snake, lizard, bull, dog, lion, toad and monkey chimeras.
In Dragon Ball Z there are a couple of notables. Captain Ginyu, of course, is turned into a frog when Goku interrupts his attempt to swap bodies with Vegeta by tossing a frog in the way. Saiyans with tails will, when looking at the full moon, turn into very large apes. Also inverted during the 22nd Tenkaichi Budokai, when we meet Man-Wolf. He was a humanoid wolf who turned into a human during the full moon. When Jackie Chun previously blew up the moon, it left him stuck in wolf form, and quite angry about it. So, Jackie hypnotizes him into his human form permanently.
In Bludgeoning Angel Dokurochan Dokuro has a bad habit of doing this to students who get in the way between her and Sakura. One she turns into a baboon, the other an Shiba dog. No one seems to care. Made extra-funny by how they render the change: replacing the characters heads with paper cutouts, as seen here.
Some characters in Ranma One Half are cursed to transform into animals when doused with cold water. We get to see a giant panda, a cat, a piglet, a goose and a yeti-bull-crane-eel-octopus hybrid. The degree of "involuntary" varies, though.
Thor was turned into a frog once because of a curse by Loki.
And don't forget The Shaggy Dog on the live-action end.
In the Kim Possible, episode "The Full Monkey", Lord Monkey Fist curses Kim with a magic amulet, which causes her to develop a monkey-ish physique... on school picture day. Monkey Fist himself is part monkey due to radical experimentation.
The short story "The Fly" and its two movie adaptations are a high-tech and horrific version of this, where either a man and a fly exchange heads, or a man slowly becomes a fly.
In fact, this is a staple of horror and sci-fi films from the era, as evidenced by the titles "The Alligator People", "The Ape Man", "The Bat People", "The Brooklyn Gorilla", ad infinitum...
Quite a few of the characters in Stardust get turned into animals under a number of different circumstances. A farmer is turned into a goat by the wicked witch - and then on top of that she changes him back into a human later. A female human! If that's not enough, she turns another goat into a man to act as his/her father. The protagonist is turned into a dormouse by another witch, but only because he's easier to carry in her wagon this way and she changes him back as soon as they reach their destination. Finally, a fairy woman changes into a jay and back, though it's not made clear if this is under her own power or not - there are a lot of odd things going on with this character.
The book makes it quite clear that the fairy woman's shapeshifting is involuntary. This probably applies to the film as well.
In The Thief of Bagdad, Abu the thief is changed into a dog by the wicked Jafar. Curiously, he adjusts rather well to his new life, accompanying his blind friend as a dog guide.
One of the first stories of Ovid's Metamorphoses involves the transformation of Io into a white cow. Considering that this story was old by the time Ovid recounted it, this one is definitely Older Than Feudalism.
And another set of Metamorphoses, this one by Apuleius (second century CE), involves a young man, Lucius, who experiments with a witch's charms in her absence and ends up as a donkey.
Franz Kafka's The Metamorphosis; the protagonist has transformed into a bug (literally "vermin"), possibly a beetle. If that's true, it adds a layer of irony to his death: he could've flown away, if he only knew...
The Dresden Files: Using magic to transform someone else against their will is against the laws of magic, but possible. The Loup-Garou from Fool Moon is subject to a hereditary curse which causes the afflicted to transform into a nigh-invincible wolf monster and go on a rampage during a full moon.
The Librarian of Discworld's Unseen University was transformed into an orangutan early in the second book, The Light Fantastic, by an exceptionally powerful spellbook. (Books on magic are dangerous as they are, but this one belonged to the Disc's Creator) He has since come to enjoy his new state, as the prehensile toes make shelving a dream, and the muscles capable of unscrewing someone's head off. (Which he will do if you call him a monkey) The other wizards allow this because he's the only one who can run the library, and there's no rule against an ape serving on the college council (and the wizards looked very hard for one).
The Toad in the Tiffany Aching books is actually a lawyer who got on the wrong side of a fairy godmother, and subsequently got on the right side of the Nac Mac Feegle. The Disc will never be the same again.
Snow White and Rose Red, a fantasy novel adaption of the fairy tale of the same name, reveals this as the fate of a Faerie who loses their magical essence. Thus, when Hugh is robbed of his essence by humans seeking to master Faerie magic, he slowly and painfully turns into a bear over the course of a month. Furthermore, anyone who fully transforms gets unceremoniously dumped out of the realm of Faerie and banished. Hugh's curse serves as the conflict of the novel, and his loss of humanity as time passes in the bear's form becomes another source of problems.
In Buffy the Vampire Slayer, Amy, the witch, turns herself into a rat to escape an angry mob. This is on the involuntary list because she can't change herself back - as a rat, she has no powers. Amy first used her rat spell in an earlier episode on Buffy, which she later reversed.
After witnessing this, Willow and Buffy try to frighten the mob into letting them go.
Buffy: Yes! You will all be turned into vermin. And some of you will be fish! Yeah, you in the back will be fish!
Merlin had Freya, the Druid girl cursed to transform into a panther, albeit a winged one, every night at midnight.
One of the films shown on Mystery Science Theater 3000, "Jack Frost", was a bizarre pastiche of nearly every Fairy Tale Trope imaginable. In one of the many plot threads, the hero is turned into a bear - and he spends nearly the entire first half of the movie complaining loudly about this.
One of Sam's leaps on Quantum Leap was into a chimp at NASA.
However, it should be noted that Sam leaps into people's auras, not their bodies, so all the other characters see a completely different character. Sam can, in fact, stand perfectly upright in the episode, but after a scientist remarks that this is unusual for a chimp he spends the rest of the episode hunched over.
Calvin and Hobbes happily plays with the Cursed with Awesome aspect of this Trope at least twice, via Calvin's Transmogrifier. In one story, Calvin is turned into an owl and isn't pleased - until he remembers that owls don't go to school and so he and Hobbes can play in the woods all day. And then, next morning, he learns that the effects of the Transmogrifier wear off overnight. At the end of the story arc where Calvin clones himself several dozen times, he ends up transforming the clones into worms. And their immediate reaction, rather than being seriously upset, is "Cool! Look at us! Let's go gross someone out!"
Another instance is he once used the Transmogrifier to turn into a tiger, which he ended up looking like a smaller version of Hobbes.
Peasant: I want you to put a curse on my insurance man.
Wizard: Zooley-zooley-zat, your insurance man is now a rat!
(Peasant answers his door to find an enormous rat standing there with paw outstretched.)
Rat: Your premium is due...
In BIONICLE, Metus is transformed into a snake by the Mask of Life.
Vivisector: Beast Within deals with Doctor Moreau-like half-human animal cyborgs, but there's also hints that their creators also did something to the game's protagonist as a kid, which manifest during the events of the game.
Glenn the Frog of Chrono Trigger was transformed by the Big Bad. Given the some of Frog's skills explicitly take advantage of his new shape (water magic, grabbing enemies with his tongue, twenty-foot leaps,) this falls square into Cursed with Awesome.
Mario & Luigi features an early game boss fight with a dragon that hatched from a giant egg. After defeating the dragon, it turns back into main character Prince Peasley, who reveals that Cackletta turned him into the dragon and trapped him inside the egg to get him out of their way.
In the adventure game Loom, the ultimate punishment tor Spellweavers — "Transcendence" spell — involves transformation into a swan.
The manual explains how the protagonist's mother got transformed shortly after his birth.
His foster mother gets transformed into an egg shortly after the game start (the spell went wrong). Later she hatches as an adult duck.
Immediately after she becomes an egg, a swan appears and transforms into swans the whole village except the protagonist.
At the beginning of the first game, Daxter is turned into an ottsel after being knocked back into a pool of Dark Eco by accident. The plot of the game is to find a way to change him back into a human, though in the end, he is forced to give up his chance to allow Jak to defeat the Big Bads. He has since accepted his new form.
Near the end of the third game, Count Veger demanded that he'd be transformed into a Precursor when Jak is given the chance. One reveal later, he's stuck as an ottsel and at the mercy of Kleiver.
At the end of the third game, Tess is turned into an ottsel when she wishes she had pants like the ones Daxter just got.
Zoe from Sluggy Freelance is in something of a grey area between voluntary and involuntary shapeshifting. The magic tattoo on her neck causes her to transform into a camel whenever someone says "shupid" near her, and it changes her back when someone says "kwi." Technically, Zoe could say "shupid" and turn herself into a camel, but this is pretty unlikely since she doesn't like transforming and, in camel form, she can't say the magic word to change back.
She did it once, when she needed to hide fast and a random camel in a closet wouldn't raise eyebrows.
In Kevin & Kell, the portal from Earth to Furth transforms humans into appropriate animals. Except Martha, when she was hiding in a lead-lined barrel.
An apparent running gag in Electric Wonderland involves Aerynn turning NJ into a random animal whenever she needs help protecting herself and/or their teammates.
In El Goonish Shive, Dan once turned Melissa into a cat in a filler strip (which got carried over into a later filler strip).
In an April Fools strip, the cast was turned into cats at one point.
An interesting example happens in Crimson Flag, where the normally anthropomorphic fox characters are turned into normal foxes. This is more going from a Petting Zoo Person to a normal animal.
The entire basis for the Paradise setting is the involuntary (and invisible) transformation characters go through into Funny Animals.
Professor Crow from SCP Foundation was turned into an intelligent dog, presumably by a lab accident.
Jackie Chan Adventures features the Monkey Talisman which allowed the user to transform any object (living or not) into any animal (except transforming stone or rocks would create animal statues instead) and back again. Whether voluntary or not usually depended on the situation.
Jade also suffered two additional transformations during the series, once turning into a cat person after being scratched by a magical artifact, and another time turning into a donkey due to a chaotic spirit.
American Dad!'s Klaus is an East German Olympic ski jumper, semi-permanently placed in the body of a goldfish. Apparently, the fish got his body in the deal, but couldn't use it.
Kim Possible: Kim was turned into a monkey, and Ron was turned into a beaver (though not in the same episode).
The Fairly OddParents: Cosmo and Wanda frequently turn into animals to disguise themselves to keep up the Masquerade. No one seemed to care or even notice that their fur/plumage is green and pink.
One episode had Timmy trading brains with a dog, only to find himself unable to change back, since the fairies couldn't speak Dog.
And while the turtles themselves don't count, their master Splinter does, as the same ooze that turned them into humanoid turtles turned him, formerly a ninja master named Hamato Yoshi, into a humanoid rat.
Baxter Stockman turns into a fly when entering a portal at the same time an actual fly does.
The ooze does this in the 2012 series. It seems that the ooze turns a person into an animorphized version of whatever living thing (plants included) that they were last in contact with. (excluding mutants)
Beast Wars inverted a large part of the trope. Where most heroes use animal forms to become stronger, these Transformers use them to mainly protect themselves from local radiation, and can only spend limited time in the "human" (humanoid robot) form that has the real power: their guns.