We've owned and worked with several exotic animals (animal rehabbers here) but what I'd really REALLY like to have is a Kestrel. They're wicked little hunters and can be trained to return... not to be stuck in a cage.
I've had a few exotic animals: birds, a hedgehog, and turtles. The most important things to consider about exotic pets is how long they live, how much they cost to care for, how much social interaction they need and how much effort it takes to care for them. I wouldn't recommend any of the animals I mentioned.
I'm not sure if you would consider rats exotic pets, but they were some of the best pets I have ever had, but they unfortunately don't live very long.
I've always thought it would be neat to own some sort of exotic large animal as a pet, even though it is entirely too expensive and an extremely dangerous idea. Would you do it? What would you own?
We had a wolf, years ago. Adopted as an orphan baby, we had to get a special state wildlife permit. Long story, but bottom line, ours really was a dog, but a very skittish, and not very social one, with anyone but us. I don't recommend wild animals (even hand raised) as pets.
Nothing as huge and troublesome as a tiger. Not looking to have my face ripped off. Plus the cost of feeding one, having big enough area for something like that (with strong cage so didn't get out), and keeping it entertained - I can't even imagine
Little not-so-normal pets though... fennec foxes, sugar gliders, wolf mixes, MAYBE even capuchins or other smaller primates can be fun and interesting pets as long as you take good care of them