I would love to keep big cats but lets be realistic... not possible for 99.9% of us coz of laws (not easy to hide a cougar or tiger in your home and still be able to give it the best care.. kinda dangerous too). So I think it would all come down to what one can hide from the bylaw officers.
I would love to keep a couple of flying foxes (fruit eating bats) they look like cute little dogs with wings. I would get myself a Harris Hawk (I'm getting one next year) and maybe a Macaw or two.
I would not get a monkey... they are generally a pain in the arse to keep... too mischevious ( throw their poo at you and just make a complete mess of things).. although I do think them little Squirrel monkeys are really cute.... yeah maybe I would get one of those.