Hmm....people I've lived with and their pets, let's see if there are any correlations:
Me - INTP - prefer cats, dogs are OK, can get along fine without a pet.
Dad - ISTP - likes dogs & cats equally. Loves animals, has also kept birds, fish and rodents as pets.
Mom - xSFJ - Strongly prefers dogs, will tolerate cats but doesn't like them to be in the house, ever.
Sister - ISTJ - Definite dog preference but not as strong as mom's. Pet-crazy. Her pets are her kids. Strong into animal rights causes.
Ex #1 - ISTP - prefers cats but also likes dogs. Animal lover. Works in veterinary medicine and loves it. Last I heard she had 5 cats, a dog, and a fishtank.
Ex #2 - ISFJ - Dog preference but likes cats. Almost, but not quite, parent-child type relationship with her dog. Must own a dog at all times.