The only two requirements for a pet in my life at this time. But I can't really think of any I wouldn't have. Probably not anything too small or too big. And although I prefer furry animals, I wouldn't reject one with a different type of skin or coat.
For their sake, I think the only pet I wouldn't have is fish. As I said, for their sake - I have had bad luck with caring for fish in the past and wouldn't want to harm any more through my own ignorance.