Our Werebeasts Are Different: Mythology & Religion
Boar (Greece and Turkey)
Wolves (All over the place, naturally. Special mention goes to the werewolves of Russia and Scotland, which are thought of as being simply another "race" or "tribe" of people who happen to have the ability to turn into wolves, rather than witches who made a Deal with the Devil)
Dog (New Guinea)
Tiger (India, Malaysia, Borneo, China and Japan)
Crocodile (Egypt and Zambia)
Bears (North America)
Hare (North America)
Jaguar (North/South America)
River Dolphin/Boto Encantado (South America)
In French-Canadian mythology, the therianthrope is usually a man who has failed to perform his religious duties for several years straight, often seven. They were then either cursed to take an animal form until freed, or only at night until freed. In most case, the curse can be broken by a neighbor pricking the were's skin with a needle. Legends have been recorded involving people turning into wolves (either full wolves, or a being with the normal form of a wolf but walking on two legs), dogs, hellhounds, cats, imps and at least one pig.
In Japanese mythology, henge, a subset of youkai, are magical animals with Shapeshifting powers and human intelligence. They often assume human form and get into all kinds of mischief. Examples of henge should go on the Youkai page.
The "Animal Wife" motif which has an animal shed its clothes and become a beautiful woman and often be taken as (or become) the wife of an ordinary human. This includes beings with specific names (Selkies in Iceland and Ireland, Swan-Maidens in Germany, Russia and other area off Europe), but most are just known by their animal form. Examples include Doves (Italy), Wolves (Croatia), Buffalo (Africa) and Cranes (Japan). It also has crossed over to other beings such as (in Japan) divine ones (Tennin, literally "Heavenly Being").
The Native American Skin Walker is either a human sorcerer who can take animal form, or a spirit being of incredible power that can take various animal forms. The details vary, but they are considered to be one of the most evil of all monsters.