Legend has it that when Chang San Feng, creator of tai chi, witnessed a snake and crane fighting, he decided that the key to developing superior martial skills resided in copying the soft and coiling techniques of animals.
As far as I understand it, however, the concept of emulating animals goes back thousands of years prior to the advent of tai chi in the 12th century AD. The ancient arts of qigong and hsing-i - the way of the mind and will - both use animal forms to stimulate healing in each of the body's organ systems and take advantage of a unique style of movement in order to develop devastating attacks and defenses. If you're curious about the kinds of animals involved, you need look no further than the Chinese horoscope, which lists them: rat; ox; tiger; rabbit; dragon; snake; horse; sheep; monkey; rooster; dog; pig.
It's well worth studying which animal signs are compatible with others, and which signs clash according to the horoscope, since those correspondences and oppositions will tell you just about everything you need to know about which animal fighting forms oppose which. For example, my Chinese sign is dog. I'm not supposed to get along with dragons, according to most Chinese astrologers. Not coincidentally, when sparring, the coiling, sinuous dragon movements can be counteracted by the downward strikes of dog.
It's well worth turning to animals to observe how they move. I learned how to fight like a dog by playing a version of push hands with my own dog. Watching how rapidly and effectively he knocks my hands down taught me a lot, as did his tenacity.
Note that some of the horoscope signs correspond to more than one animal. Dog is bear in some systems, while cat and rabbit share a category. (Both of these animals do tend to try to gouge with their back paws, so I guess there is some similarity.)
For inspiration, check out this slow motion video of a kitten playing with a feather toy and sparring with a human hand. Watch the position of his forelegs, the stretch in his paws, and the way his spine moves supply as he attacks the toy and tries to grab it. You could do far worse than cultivate a similarly stretched out paw / hand and loose spine!