The entire point of The Immortals quartet by Tamora Pierce. Daine has Wild Magic, allowing her to communicate with, heal, command, and change into animals. Stemming from her minor god of a father, the books deal with her bringing her powers under control. She can also partially shapeshift, doing things like putting her human head on an eagle's body. Though sometimes her clothes go with her when she shifts, and sometimes not.
Two prominent examples in Harry Potter: Animagi use a complicated spell to turn into a specific animal at will. Animagi are supposed to be registered with the government, but there only 7 such registered individuals, only one of whom appears in the story. Four unregistered individuals either appear or are mentioned in the story, so it seems likely the actual number is considerably higher. By contrast, metamorphmagi have an inherited at-will ability to change their appearance any way they wish, but with limitations on shape, so changing species is out of the question. Talented wizards and witches in general can transform themselves on a more temporary basis. There are spells and potions for shape-shifting — their mastery is required for becoming an Auror.
Werewolves can shift between human and lupine shapes at will, although during nights of full moon they're forced into their wolf shapes.
Many vampires can change into a bat, a number of bats, or a number of magpies (in the case of the de Magpyr family). Some (again, the de Magpyr family) can also become a sort of gaseous form. Whether they keep their clothes or not depends on their sex, due to the fact that Rule of Sexy, like many other tropes, is a kind of natural law on the Discworld... as is, apparently, the Male Gaze.
Animorphs: The protagonists have the ability to absorb the DNA of any animal (or alien) they touch, then transform into it, thanks to Imported Alien Phlebotinum. There are a few limitations that every morpher is subject to: First, they can't go directly from one morph to another, needing to change back to their original form before they can use another one. Second, DNA can't be absorbed while in morph, nor can it be absorbed from a morph. And third, staying in morph for any longer than two hours will cause the morpher to be trapped in morph, unable to morph at all.
Beorn from The Hobbit can transform into a bear at will.
In The Silmarillion, Finrod Felagund disguises himself, Beren and their companions as orcs, probably by singing (which is how Sauron later strips them of their disguise). A little later, Lúthien turns Beren into a werewolf and herself into a bat-like creature.
This is a standard ability of all Ainur with a couple of exceptions. The wizards gave it up as part of the limiting of their powers, and Morgoth was Shapeshifter Mode Locked into his Evil Overlord form because he became too attached to it. Sauron was noted to have a particularly strong talent at this himself, being able to even deceive elves or Númenóreans, though after the Downfall of Númenor he lost the ability to conceal his true nature.
The race known as the Shi'ido can shape-shift into humanoids of any species, including specific individuals, as well as animals of various sizes.
Clawdites can also shapeshift, but it's less effortless.
The 2012 Essential Guide to Warfare states that the Celestials were "of malleable form".
Tofu from Super Minion. His micro units can reshape his flesh at will, allowing him to repair injuries and shapeshift into any roughly biological form.
Kiesha'ra: Shapeshifters, known as Elavie, usually have the ability to change into only one animal, sometimes with a half-form as well. Particularly strong vampires can shapeshift as well, but unless the vampire was Elavie before being turned (such as Jaguar), it's more a case of having a very good sense of self and an understanding of one's own shape and the shape of the animal.
Many creatures in the Mercy Thompson series can change shape voluntarily. The titular character can turn into a coyote at will, there are werewolves aplenty, and all fae can disguise themselves with basic illusion magic.
Saint Dane in The Pendragon Adventure can shift into nearly any form suited for any Territory, even if the Territory is inhabited by cat people (which Eelong is). Sometimes he creates an alias, sometimes he steals one, sometimes he even changes genders. He also has the form of a black crow for quick movement. If it weren't for his icy-blue eyes and tendency to want to reveal himself, he'd be near-impossible to find.
Journey to the West: Sun Wukong the magic monkey has among his many powers the seventy-two transformations, which allows him to transform into absolutely anything. Also worth mention is Zhu Bajie (aka Pigsy) who only knows thirty-six transformations, half as many as Sun Wukong. He makes up for it with being better at fighting underwater (despite being a Pig Man).
The main characters of Switchers, by Kate Thompson, have the ability to transform into any animal they wish at will... at least until they turn 15.
H. P. Lovecraft's Nyarlathotep is an interesting case. He has over 1000 different forms, although it's never really made clear whether he can switch between forms or is he stuck to the one he manifests in. It might also be possible for him to manifest in more than one form at once (being the herald and soul of the Outer Gods means he can ignore pesky things like the laws of our space-time continuum). While it's not quite clear whether or not he can switch between forms, some of his forms are able to shapeshift.
In the novel "Shifting" by Bethany Wiggins, both Maggie Mae and Bridger can voluntarily turn into animals. Bridger can turn only into a golden eagle, and the eagle's love instinct remains. Maggie Mae can turn into virtually any warm-blooded, carnivorous animal because her mother was a shifter, but her father was a skin walker. Since one of Bridger's parents was a shifter and the other one was normal, if he tries to turn into anything besides a golden eagle, he will die. Their clothes don't change with them, so this causes many problems, especially for Maggie Mae.
The goblins in the J.W. Wells & Co. books can shift instantaneously into any human form, although whether they can take other forms has not been mentioned. The vainer goblins in the series, such as Rosie Tanner, enjoy transforming into a different supermodel-gorgeous human every day, wearing bodies the way some Hollywood film stars wear clothes — always the best, and never the same outfit twice. It is emphasized that while goblins actually change the structure of their bodies, other creatures like the Fey prefer the simpler methods of glamour and illusion, which take less magical strength than actual shapeshifting.
The Eastern-style Dragons in Nothing But Blue Skies can shapeshift to become human, or, um, goldfish.
In Falling Sideways, the super-intelligent alien frogs can take on human shape at will.
The character of Emma Anyanwu from Octavia Butler's Patternist series has total conscious control of her body at a cellular level. She can regenerate from any injury, stop herself from aging, alter her DNA at will, and take the form of any human or animal regardless of gender. Although she can mimic the outward appearance of any creature she sees, to become a truly accurate replica of another living organism she has to ingest and analyze a sample of that organism's DNA, e.g. through a bite of animal meat or a drop of blood.
Memory, Sorrow, and Thorn: Geloë is a practitioner of what might be regarded as druidic magic, including the ability to shapeshift, primarily into birds. Handled fairly realistically in that it does not affect her clothing.
Happens a few times in Fable Haven. Unicorns and dragons are known for taking human form, and potions can shrink people down to doll-like size. And the Eternal's eternal guardians, ageless sentient talking animals that can sense their charge's location, turn into any animal with approximately the same mass, and can only be killed by powerful magic, such as phoenix flame, dragon fire(or bones), and other such weapons.
Dax Jones from The Shapeshifter series can take multiple animal forms, like his alien mother's species and has to regularly or suffer stroke like symptoms.
The Kandra from Mistborn can change into anything they want — but they can't produce a rigid skeleton. Because it's almost impossible for them to replicate an individual's features without digesting them first, they generally just use the original bones anyway. Among themselves they use metal, stone, or wooden skeletons called "true bodies" which particularly creative Kandra often make into wild and fanciful shapes to show off their abilities.
They aren't limited to humanoid shapes, either; it's just something of a taboo, because they consider it extremely demeaning to be forced to wear nonhuman bones. One of them is forced for a time to wear the bones of a wolfhound, and he eventually grows rather fond of the form, mostly because of the physical advantages (speed, natural weapons) of being in the body of a big damn dog.
The Dutch YA novel De Wortels Van Het Woud (The Roots of the Forest, by Tais Teng) has a main character who can modify his body with various animal characteristics. It turns out that he and his sister are among the last of a race of shamans. Although his sister (whose powers are not related to shapeshifting) is utterly freaked out by the revelation, the boy eventually chooses to stay in the world of magic and live his life in the Forest in millions of animal forms.
The si'lura in The Banned and the Banished by James Clemens are a race of Shapeshifters that are able to take the form of any living creature. They are also able to communicate in any form through an image based telepathy that requires eye to eye contact. Spending too long in one form can cause the shifter to settle and be unable to change again.
Wild Cards: Several Aces, such as Mr. Nobody, gain the ability to shapeshift to a greater or lesser degree.
In The Dresden Files, when self-inflicted this is the only type of shapeshifting that doesn't violate the second Law of magic. Any transformation of another, either by force or benign, is not allowed. Among the non-violators are the Alphas, who have the ability to turn into wolves voluntarily (in contrast to the loup-garou, which transform involuntarily, and the hexunwulf, which is reliant on an Artifact of Doom). Also the skinwalker and Listens to Wind.
The Soletaken are individuals with the ability to assume animal form. Most assume mundane forms, such as wolves or bears, but Eleint Soletaken possess the rare ability to assume the form of a dragon. There also exist the D'ivers Soletaken, who can split their mind into several transformed bodies.
Azathanai don't have a fixed physical form, so they can change their appearance at will. Skillen Droe in The Kharkanas Trilogy takes the form of a flying raptor, while K'rul seems to change his gender every few hundred years.
Watercrafters in Codex Alera can change their appearance if they are skilled/powerful enough. It's limited to human forms, with it being difficult to hold a form with a significantly different height/build then the crafter, and generally used to maintain a youthful appearance.
Immortals in The Madness Season are able to transform into any creature that originates from Earth. The Marra are able to go one better and transform into any living thing that can exist, no matter what their biochemistry.
"Demons" in The Bartimaeus Trilogy are actually spirits summoned from another plane of existence where there are no physical forms. While on Earth, they're constrained to a physical body of some kind, but it can be pretty much whatever they feel like. Generally they take humanoid or animal forms, whatever fits the situation, but there's plenty of examples of mythological creatures (phoenixes, ogres, etc.) or hybrids involving whatever body parts they feel like, and even the implication that they could probably take the form of inanimate objects, if they so desired. The only real limits are that excessive shifting will wear them out eventually. They also seem to be somewhat constrained by size, never getting much bigger than slightly bigger than human size (although the more powerful the demon, the larger they are).
In the Apprentice Adept series, all unicorns can choose two other shapes they can change into at will. Most of them seem to pick human and a winged form.
The Last Dove: Every single character can do this. Some clans will shun those who can't.
Generally speaking, all gods can take whatever shape they please.
In the The Heroes of Olympus series, Frank Zhang can turn into any living thing. He needs to know the animal well, though. He inherited his powers from his distant ancestor, the Greek hero Periclymenus, who was given the ability to take the shapes of animals by his father Poseidon.
In the Xanth series, Prince Dolph's magical talent is being able to transform into any living thing (including borderline cases like zombies). Certain species of crossbreeds have this ability as well, but it's more limited. For example, a naga can shift from their default form of snake with human head to full human or full snake, and merpeople can turn their tail into legs. In one book there was a dragon/human girl who could shift from the default form of dragon with human head to full dragon or full human.
The Proteids in the Arrivals from the Dark series are a race of shapeshifters whose normal form is a shapeless pile of flesh. Most are able to shift at will to mimic any race (down to internal structure to fool any scan) and even specific beings. Due to their nature, they are, essentially, immortal. After all, what is aging to someone who can simply turn into a younger version of himself? They are also able to recover from massive damage. They are pretty neutral and prefer to stay hidden. They still send out emissaries to secretly monitor a given race and, occasionally, help or subvert them for the good of the galaxy at large. One of the key characters is a Proteid with a birth defect. He can only morph into a species once, at which point he is stuck as that form for the rest of his life, able only to affect fairly minor changes (height, skin color, body shape). Even turning into a member of the opposite sex is impossible, as that involves major changes to internal structure. Named Exile for this defect, he chooses to go to Earth (in the 13th century) as an emissary, as his people see the potential in humanity. He assumes the form of a human male and begins to observe humanity.
Majipoor Series: The Piurivar or Metamorphs, who are one of the native species of Majipoor, and have been at war with humanity for almost as long as humanity has been on the planet, can shapeshift to resemble almost any vaguely humanoid species. If it weren't for fairly reliable Metamorph detectors, humanity would probably never have had a chance.
In Demon: A Memoir, demons can change shape. The titular character takes on the form of a different human every time he meets the narrator.
In Satan's Diary, the last of novel by L. Andreyev, the protagonist tries to take a human form for the first time.
The Parshendi have a minor version of this: they can shift between certain specific forms by bonding appropriate spren to their bodies. So far, they have learned how to assume dullform (weak and stupid, their baseline state), mateform (lust-crazed, capable of reproduction), workform (strong, but with a mental block against confrontation), warform (strong and aggressive, with natural armor plate growing from the skin), and nimbleform (dexterous and agile, useful for precise work). And in Words of Radiance, they learn how to assume stormform, which grants Shock and Awe powers but leaves them Ax-Crazy. There are a number of other forms that appear in Oathbringer as well, although they're not all given names or explained in detail.
Also, once a Surgebinder has sworn enough oaths, their bonded spren can assume the form of a Shardblade. Or a Shardspear. Or whatever other metallic item their Radiant needs. Existing Shardblades are "dead" spren trapped in that form after their Radiant partners broke their oaths and walked away.
The shapeshifters in several Sharon Green novels could shift into anything from animals to fruit, given sufficient practice. Most people had a couple of basic forms, with full-range shifting or something close to it showing up more often in nobles and prostitutes. While you could change your size and shape, however, your mass remained exactly the same.
Both Werewolf and Bedlam in Devil's Cape are able to do this as their primary superpower. Werewolf, as his name suggests, can turn into a wolf, human, or his preferred form, a hybrid of the two. Bedlam can either be human or take on a demonic-looking, superstrong form capable of flight.
Shapeshifting in the Coldfire Trilogy is theoretically possible with the fae, but no known humans have ever done it. It requires an insane amount of dedication and a willingness to cast aside your very nature as a human being. Senzei is both horrified and impressed when he watches Gerald Tarrant the Hunter transform into a bird. It highlights both his genius and the fact that, appearances aside, he cannot really be considered human anymore.
The Reynard Cycle: The Fetch are shapeshifting assassins originally created by the Demons. In their natural form they look like featureless, translucent humanoids with colorful luminescent fluids inside of them. One of them infiltrates the Quicksilver during Reynard the Fox. It's unclear if there are others existent in the world, or if that one was the last of its kind.
My stupid mouth acted on automatic. "She almost looks like Claire." Dad just chuckled. "She does, doesn't she? I think it was a half-hearted attempt to frame Claire. The name is deliberate, and the costume is a reference to her power. I say 'half-hearted', because if E-Claire were really trying she would hide her face. The first words out of your mother's mouth were 'Her cheekbones are wrong', and her body language was wrong in the first video. She can't even claim to be Claire in makeup." Claire Lutra, you little vixen. You knew all along your secret identity was completely safe. Your Mom must have known as well. And if E-Claire couldn't possibly be Claire, then her teammates couldn't be me and Ray. You devious shape-changing vixen, Claire. You'd covered us all.
Bora Horza Gorbachul in Consider Phlebas is a "Changer", who has limited (by the standards of this trope) shapeshifting powers, as did his whole race. Which is why they were wiped out.
Somewhither: The world of Cainem is inhabited by immortals whose wounds and all damage heal quickly on their own. Experienced inhabitants of Cainem can control this process and thus manipulate their body in any way they wish, including detaching limbs and bones and using them as weapons, or growing bone-armor over their skin, or even dispersing all mass of their tissues over a large volume to become a hard-to-spot cloud of thick mist.
Star Trek: The Eugenics Wars has Isis, who can can turn into an (apparently) human woman, though she stays in cat form most of the time. She spends most of the second volume pretending to be Ament, one of Khans most trusted advisers.
Masquerade of the Red Death: The Children of Dreadful Night have the ability to take on the form of any vampire they've met. The mechanics aren't clear, but apparently the shift can be made permanent — when two of the Children are tricked into burning through all their energy, they still retain the forms of the two vampires they're impersonating.
The Witcher series has a race known as "dopplers", who can assume the form of anyone (including clothing and physical accessories carried on the person) after the briefest of analysis. This ability inspires paranoia and suspicion amongst the public, but in reality dopplers are actually good-natured and are not prone to Kill and Replace schemes (though they are not above replacing someone who has already died).
Warren the 13th: The three witches have "spirit animals" that they can transform into at any time: Scalene turns into a wolf, Isosceles turns into a vulture, and Annaconda turns into a snail.
The short story "Shape" by Robert Sheckley is about an alien race which can shift into pretty much any form they want—but their society is extremely rigid and strict, and shifting into shapes which are not approved for your caste is a major taboo.
The Crimson Shadow: Greensparrow made a pact with a dragon to share his body in return for magical powers. Most of the time he can control this, but the dragon forces him to transform occasionally.
Thorn eventually learns how to change into different forms, ranging from real animals to made up creatures — though it seems he's either unable or unwilling to mimic appearance of others.
Dragon, while naturally giant winged lizards, often interact with others as humans, irks or Body Horror-ridden humanoids.
Mindwarp: Primarily the shtick of the villainous alien killers, but Todd Aldridge also has this power.
In Void City, this is a standard vampire power. Stronger vampires can transform into a variety of shapes such as bats, cats, and rats, while weaker vampires are limited to a single transformation. Froggy, for instance, got her nickname because the only animal she can shift into is a frog.
Rogues of the Republic: Unicorns can take any animal shape, including human. Ululenia usually takes a snowy white form, but she can probably change the coloration.
Villains by Necessity: Kaylana turns into a horse at one point as a disguise. Fenwick, thinking she's a real horse, tries to ride off on her. She bucks him off.
Meta Morfoss from the same-titled children book of GDR author Peter Hacks. Entirely harmless, she can turn into anything... and can be a royal pain in the butt when she turns into an angel scaring a pilot, and other assorted shenanigans.
The vampire-like Mage Species of The Shadowspawn can assume the form of any creature (the individual, as well as the species) whose DNA they have ingested, which has given rise to the werewolf and vampire myths of Europe.
Operation Chaos has Steven Matuchek, a Special Forces operative who is a werewolf. He carries a small polarized light generator that simulates moonlight so that he can transform as necessary for his work.
In Renegades, the Anarchist Phobia can transform into various fears, ranging from swarms of bugs to jets of fire.
In keeping with Dragon Pearl's roots in Korean myth, this is a thing that animal spirits can do. Gumiho (fox spirits) can shift into basically anything, including inanimate objects and other people; dragon spirits and tiger spirits can only switch between their animal forms and their human ones.
''Woodwalkers: Woodwalkers can choose any time if they walk around in their human or in their animal form although there is a secret technique which forces said shapeshifter to stay in one form. Luckily only a few people know that it exists and only around half of them knows how to use is.
During the fourth year at Brakebills in The Magicians, students learn how to transform into animals of their own accord, and once they get the hang of controlling the Shapeshifter Baggage, it's comparatively easy to turn into geese, polar bears and arctic foxes. However, Alice is the only member of the main cast that goes on to make practical use of this skill: during the final battle with the Beast, she transforms into a lion, an anaconda, an eagle, a bear, a giant scorpion, and even a dragon.
In the Splintered Series, several of the humanoid netherlings have an alternate animal form they can shift into, such as Morpheus's moth or Ivory's swan. Alyssa doesn't have one since her human form is her alternate form.
In Sheri S. Tepper's The True Game, where everybody has some kind of magical Talent, there is a class of people with this ability. The Shifters are introduced as, essentially, werewolves: clans of people whose Talent is to shift at will between human form and the form of a large predator that is this world's equivalent of a wolf. The sequel trilogy, which has a Shifter protagonist, reveals that they can actually shift into any form imaginable (and frequently hold shape-shifting competitions among themselves) but have a tradition of pretending to outsiders that they each have only one alternate form so that their enemies will underestimate them.
Barbapapa: The Barbapapas are a family of colorful blobs who can turn into any shape. They can take the shape of animals or objects, but their colour and face stays the same.
“She must have some kind of shapeshifter ability,” Cassandra answered grimly, before ordering me, “Drop it.”
“I wish I could,” I responded, still keeping my eyes locked on that arrow, which was aimed at my chest. “But I can’t.”
In Fengshen Yanyi, many characters can transform in one way or another, but The Ace in this technique is Yang Jian (Erlang Shen), who has mastered the 72 Transformations and can turn himself into any person or animal, as well as turning his body into iron, copper, gold or stone as needed and even regrow a heart and close a fatal wound like nothing and become immune to plague.
Mercedes Lackey's Firebird:The Firebird can take the form of a striking bird with Hot Wings, a beautiful woman with a cloak of feathers, or an unearthly melding of both.
Bruce Coville's Book of... Nightmares: The dragon of The Boy Who Cried Dragon has this power, and disguises itself as a cat around normal humans.
Of Fire and Stars: Karov, a Zumordan merchant and magic user, can turn himself into a bird. It later turns out it's common magic in Zumorda, with many Zumordans commonly becoming animals. Their particular animal form is called a person's "manifest", which they're magically bonded to.
Holo from Spice and Wolf is a wolf spirit who can change forms between her true form of a giant wolf and a teenage, human girl with wolf ears and a tail.
In Deltora Quest, Ols are artificial creatures capable of taking the form of any other living being, and come in three levels. Most Ols can keep a disguise for up to three days before suffering from a brief Glamour Failure, but can only be killed by having their heart pierced or through extreme means. A Level 3 Ol is so good at shapeshifting that it can stay disguised indefinitely and even transform into inanimate objects; the catch is that Level 3s are too good at shapeshifting, gaining all the weaknesses of their current form.
The Witch Of Knightcharm: The rookie witch LaTasha reveals herself to be very good at this, showing the ability to turn into a cheetah even before classes have started.