Do you mean unique animals that you can actually buy as pets, or animals that aren't pets that you wish could be pets?
As for unique animals that actually are pets that I want, I really want an axoltl, a bearded dragon, and a chinchilla. I used to have a hedgehog and I adored him but probably won't be getting another one as I developed an allergy to his spikes when I was pregnant.
As for animals that can't actually be pets, I would love a red panda and a meerkat. Oh, and as an extremely far-fetched choice, a rhinoceros! I think they're adorable and there's always one rhino at the zoo that plays with his ball like a puppy and I wish I could take him home and keep him in my backyard. :)