The two most prominent shapeshifting animals in Japanese folklore are the tanuki (raccoon dog) and kitsune (fox).
The raccoon dog is related to actual raccoons less by taxonomy than appearance. Along with dogs, foxes and wolves, tanuki belong to the Canidae family, while raccoons belong to the Procyonidae family.
In folk art, the tanuki is depicted sporting a straw hat, a bottle of booze in one hand and a checkbook in the other. They're ready to get down to business or party hearty.
This penchant for wheeling and dealing has made the tanuki a symbol of good luck and fortune, so they're often found outside retail establishments, such as this cheerful fellow advertising a restaurant.
Unlike the clever kitsune, however, tanuki don't plan much beyond the next trick. Their extraordinary skills of deception, such as conning humans with money conjured out of leaves, often end up causing them even more Grimm-style trouble.
According to an old saying: The fox has seven disguises; the tanuki has eight. In a famous fairy tale called Bunbuku Chagama ("The lucky bubbling teapot"), a tanuki transforms himself into a teapot, which leads to various misadventures.
Kitsune and tanuki often team up in folk tales, with the fox as the Dean Martin character (cool) and the tanuki as Jerry Lewis (comic relief).
Studio Ghibli's Pom Poko depicts a bunch of bumbling tanuki trying to save their land from a housing development. They inflict a lot of Road Runner vs. Coyote damage on themselves and the construction workers, but don't get much done until a smooth-talking fox shows up.
Kitsune are servants of Inari, the Shinto god of rice and industry. Although the tanuki are masters of disguise, the kitsune's greater intelligence and magical powers (signified by the number of their tails) elevated them to the heights of human society.
Many fairy tales depict kitsune assuming human form, not to take advantage of people, but out of true love and devotion. The most famous of these is "The Fox Wife." An updated version can be found in the opening story arc of the anime series Kanon.
The story likely had its origins with Kuzunoha, the mother of Abe no Seimei, the powerful Heian period astrologer and diviner. She was said to be a kitsune who bestowed a portion of her magical powers on her son.
These were/human unions gave rise to the saying "A fox wedding," meaning a downpour while the sun shines (the expression seems to have arisen in India and spread throughout Asia). Fox wedding festivals are still held around Japan.
Wolves traditionally appeared in Japanese folklore as Shinto gods (ookami) and divine messengers who occupied a world where sacred nature hadn't been tamed by civilization. Perhaps the best modern depiction of this perspective can be found in Princess Mononoke.
In his forward to The Lost Wolves of Japan, William Cronon notes that
Grain farmers once worshiped wolves at shrines and left food offerings near their dens, beseeching the elusive canine to protect their crops from the sharp hooves and voracious appetites of wild boars and deer.
But by the eighteenth century, just as in the West, the Japanese wolf came to be seen as a "rabid man-killer," and had been hunted to extinction by the beginning of the twentieth. Well, except for the werewolves, that escaped the hunter by hiding in plain view.