I think it's pretty clear that exotic animals should not be kept as pets. http://www.noahslostark.org/
I have somewhat mixed feelings about this issue. On the one hand, I do feel it would be irresponsible for the average urban or suburbanite to keep a lion in their back yard. On the other, If I were hypothetically a wealthy landowner with many acres, and I could afford to create and upkeep a private version of San Diego Zoo Safari Park with all kinds of exotic "pets"--Why not?
The most important consideration should probably be the care of the animals and safety of the facilities, not whether or not someone is a private individual or a corporate entity like a zoo.