I'm going to be deadly boring and say a horse. I am so jealous of those who are lucky enough to own one. Although the dolphin idea isn't bad one - I'd have to have a pretty big swimming pool though.
I would like to a sloth as pet. It's lame, sleeping over 18 hours per day, moves and eats hardly. Furthermore it do one's business one time per week. A sloth would be an easy-care pet. That's why I like it.
However this animal must be in freedom. So I would never think a sloth to keep as pet.