I can handle hosting pretty much anything but cats (only because I'm allergic), but my Mom lives across the street from me, and loves cats.
I probably can't get away with any cows, horses, or large exotic animals either, just because of the neighborhood I'm in.
As long as they're not too bitey, or wild I like all animals though (experience with:Birds, dogs, rodents, reptiles, amphibians, fish)!