I want an owl to perch on my shoulder. (I’m assuming it’s domesticated enough that it can do that without piercing my skin.)
Or maybe a Dik-dik. It’s already the right size for a house pet.
Oh, they are domsticatable. That’s what I would get too!
A lynx or bobcat (or just a domestic cat that big).
Oh, a capybara would be a great choice, too.
Now that I think about it, I wish I could domesticate my housecats. You know, be able to eat a meal in peace, type on my computer, not bleed a lot…
A Liger, it’s pretty much my favorite animal.
A Mtn Lion. Purrs. Keeps burglars out.
Yes please! At first I was going to say a koala, but they’re not very social. I’d love to have a wallaby that would go on walks with me.
I also want a monkey but not one that will eat my face. And it has to be small enough so that if it started to sass me I could give it a what for.
So I’d go with a Pygmy Marmoset.
If he could be toilet trained, then Donald Trump. And I would keep him in my basement and not let him out for the next 45 months.
Failing that, maybe a whale. Of course, I would need to live at the seashore. One summer when she was a little girl, my mother played with a dolphin every day of the summer she spent in Wildwood, NJ. That would have been in the early 1920s. What a wonderful treat.
I’ve always wanted a big male lion that I could snuggle up with when it’s cold.
Those chupacabras are nasty! 
I bobcat is a lynx.
A herd of massive plate-sized slime moulds, trained to communicate like the cave-dwelling creatures in The Sirens of Titan. Or a fox.
I would like a giant panda. A breeding pair of them, actually, so that I could have baby pandas to cuddle and play with.
T-rex
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Pet fossil-cool.
Yeah - rather like a wolverine, but not as peaceful or friendly.
Just like Harry Dresden! 
Seconded. They’re cute as all get out, plus I’d have it rob restaurants for my dinners; not only does it already have the mask on its face, but it eats, shoots and leaves.
When I was a kid I wanted a pet gorilla (or at least “gorilla friend”) so he could beat up my enemies. But now I’m a grown-up with no actual “enemies” and …
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Nope. Still want a gorilla.
I grew up the woods of Louisiana. We had plenty of exotic native wildlife but I didn’t really understand the concept of geography and habitat when I was 4 or 5. I assumed gorillas were going to be just as easy to find as deer, snakes, frogs or even alligators if I just looked in the woods enough. I tried to find one to bring home as a friend for days before my grandmother broke the news to me.
I don’t think it’s just a regional name thing, I think they really are considered separate species.