I once had a riding trainer who owned a Vietnamese pot bellied pig as a pet. Not a MINIATURE. A full sized one. (Which is still fairly small...for a pig. But still a pig. A full-sized pig).
I know several people who own snakes of various kinds.
And I used to know a falconer and owler who recommended that if you want an owl just as a pet, you should get a Tawny Owl because they're lazy and won't do anything but sit around all day anyway - useless for falconry, but great decoration ;). (She also had a buzzard, a pair of Turkemenian eagle owls, a barn owl and I think a kestrel. But those weren't PETS...those were working birds).
I also know somebody who used to keep sugar gliders, which are apparently easy to feed and care for, but need a fairly large aviary to be truly happy.