Pegasus! Pegasus!

My mythical pet would definitely be a pegasus.

I've always really liked horses, and I took riding lessons for a few years when I was in junior high and I loved it.  And pegasi are just like horses except cooler.  They have wings.  They can fly.  I think having a horse that you could ride but it could fly would be just the most amazing thing.

The difficulties of caring for a pegasus would mostly depend on how smart it was.  I mean, taking care of a regular horse isn't exactly easy; there would still be all the feeding, grooming, stall-mucking, hoof-caring, etc.  Plus I guess I would have to train the pegasus to let me ride it.  But the biggest issue would be whether it was smart enough to stay home, or at least to come back home.  If it was, then it wouldn't really be a big deal, but if it was going to go out and get lost or run away all the time, then you'd have to build some sort of enormous cage/building to keep it in, and that would be a hassle.  Plus you'd have to keep it climate-controlled and everything, and heating/cooling large spaces is expensive.

Overall, though, I think the pros would outweigh the cons, and that a pegasus would make a pretty fantastic pet.