There seem to be two different types of answers going on in the thread so far: what animal would you like to be, and what animal is most like you.
Like to be: probably a cat. Who wouldn't want to run the household, sleep 20 hours a day, and then basically lie around for most of those four hours that you're awake?
Most like me: I guess maybe a chipmunk? Skittish, sees others as a source of anxiety, and prefers to stay away from everyone. Unless you're kind, and *very* patient--plus free food always helps--and then maybe I will slowly warm up to you, and come and be your friend... but only expect me to get together for short periods at a time. And don't make any sudden moves.