I would want a Russian boar or an elephant. Fortunately wild boars are easy to get if you can buy a piglet from a game rancher, elephants... not so much anymore.
Owl or fox would my dream pet, bit tehy are so fickle, hard to take care of and the paperwork plus legal stuff to get one as pet is just so much hassle. So it's no-go for me.
Another dog is coming soon, so there is that.
I've always been a big fan of the idea of owning exotic pets; in particular, I absolutely adore Fennec Foxes and would just love to have one for myself. They're friendly, playful, and just freaking adorable! They're a bit destructive though, and extremely high maintenance, which is the main thing.
I want a cat. A black cat that I can call Luna or an orangish one that I can call Pumpkin. I want them to be fluffy but even if they don't have some poof I will love them all the same. I wish I could afford to take care of a pet, but I don't have the money and I don't think I fully understand the responsibility yet, either. Maybe one day.