Hengeyokai
Hengeyokai are a category of monster (or "yokai") within Japanese mythology. Technically a subcategory of obake (shapechanging monsters), although the terms are often used interchangeably, hengeyokai is a generic title used to cover an array of monsters based on the idea of magical animals who can transform into human form, and often times into other shapes as well.
The most iconic hengeyokai are listed below. Less famous hengeyokai include the likes of Unagi-hime (female eels that take on human form), Sazae-oni (seasnails that use human form to lure in victims), and Jorogumo (giant spiders who, again, like to use the form of being beautiful human women to lure in victims).
Kitsune: Without a doubt the most iconic of all hengeyokai, the kitsune is a shapeshifting fox, often described as gaining multiple tails as its power increases. Cunning and seductive, but as likely to help humans as harm them, it has achieved a great deal of fame. A common myth-related saying suggests kitsunes tend to have seven different forms they can assume.
Tanuki: As popular as kitsunes in its home country, the tanuki myths have had a hard time getting abroad, mostly because of a certain bowdlerization issue. See, the jolly and happy-go-lucky tanuki are considered symbols of good luck, which is most prominently manifested in their enormous ball-sacks. Add in that the real animal, commonly known as the "raccoon dog", only exists in Japan, sometimes leading to translators referring to them as "raccoons" or "badgers", and they've had a hard time getting known. Ironically, although typically depicted as more oafish and goofy than the sleek, elegant kitsunes, tanuki are even better shapeshifters, able to assume eight different forms - which may not be accounting for the stories of them turning their scrotums into things like the shop around them or a palanquin with servants to carry them about.
Bakeneko: Shapeshifting cats are one of the most famous of the "lesser" hengeyokai. In fact, there are three different varieties of bakeneko at the least; the common bakeneko, who can be benevolent or malevolent as it sees fit; the two-tailed, always malevolent nekomata, who love to enslave, kill and eat people; and the kasha, particularly large and fiendish bakeneko who have a taste for corpse meat and are often servitors of hell. All varieties are known for having fire-creating and necromantic powers in addition to their shapeshifting.
Mujina: are shapeshifting badgers, very frequently confused with tanuki in the stories, to the point it's hard to really define them. Like tanuki, they are said to be capable of eight different transformations, and they're supposedly very shy and reclusive, which makes them much more careful about not giving themselves away when they do decide to walk amongst humans. Ironically, this means that Japan's badger-spirits have an attitude closer to the typical D&D elf, despite being more thematically associated with the dwarf.
Itachi: Without a doubt the most obscure of the "true" hengeyokai, itachi are shapeshifting weasels feared for their potent non-shapeshifting magic, which includes hypnotising people to become their slaves and gathering in groups to create huge firestorms. They are said to be the masters of shapeshifting, attributed with wielding nine different forms. Their cousins the Kamaitachi, a trio of super-fast weasels who run around knocking people over and cutting them with sickles, are much more famous.
Kawauso: A more obscure hengeyokai, the kawauso are jovial and friendly shapeshifting otters, who mostly take on human form to play tricks and buy booze.
It goes without saying that Dungeons & Dragons has tried to use the hengeyokai concept before whenever it does its "Oriental Adventures" splatbooks. However, rather than taking the individual types of hengeyokai and making distinct races out of them, D&D traditionally just makes a single generic "hengeyokai" race and gives it variable abilities to cover whatever animal forms it includes. Whatever you have to think about this idea, at least they've stuck to their guns on it; this version of the hengeyokai "race" has appeared in every edition from 1st through to 4th.