I'm allergic to fur, dander, spit of any animal-kind, so that limits my options a bit. Fish are wonderful; I've let my share have me as their pet. I had a turtle once, but it died because we fed it too much shrimp :(
But the elephant, well. When I was a little girl (back in the '60s, for crap's sake), the Seattle Zoo had a baby elephant at the petting zoo, and I was in heaven! First time I can remember I could actually mingle with the animals. What I wouldn't have given to bring the thing home.
Ever since, I've had a soft spot for the big creatures. And an icon of one with it's trunk up is good luck, you know.