Chimp. Bonobo or common will due. They’re the most like us of any non-human animal, and if “domesticated” they could do all kinds of helpful things around the house and yard. And they’d be fun to hang with.
I’d do anything just to get my best friend Blackjack back. He crossed the Rainbow Bridge last year and I miss him terribly. I can’t imagine any other species turning out as well as a good dog.
That’s a neat idea.
I recall a thread about barnyard animals where various Dopers described owning goats. One described having a goat as like your drunken frat brother who was always into hijinks over something.
I see a chimp as sorta like that goat but with more IQ and opposable thumbs. That’d be really cool. Until he decided to eat your face anyhow just for shits & giggles.
A fennec fox. A truly domesticated one would be fun.
Uh, you know you can’t legally keep a badger in California, right? At least not without a great deal of money/time/paperwork, and maybe not even then. CA has some of the strictest animal personal possession laws in the country, and a very good thing too, IMHO.
If you’re wanting a badger, why settle for a mere ordinary badger?
Once you’ve got the magic domesticator raygun, go whole hog and get a … wait for it …
*Honey *Badger. I hear they’re quite something. 
Yep, I’d have to get an ape. Any ape really. I’m a big fan of orangutans, and a gorilla would make a good house guard.
Commanding a troop of monkeys would be pretty cool as well. Maybe capuchins.
Oh, and a raven to perch on my shoulder.
If I had a large greenhouse with an appropriate climate, I’d love to stock it with a selection of exotic butterflies and moths. Plus the plants they’d need for reproduction.
But what I’d really want is a young and healthy version of my current black cat who’s about to cross the Rainbow Bridge.
Iberian Lynx.
one of these: Golden lion tamarin | Smithsonian's National Zoo
An army of coconut crabs trained to obey my commands. Hey, nobody would mess with me.
If extinct creatures count, I’d also like a Barbary lion or a Terror bird.
Anybody want a Wallaby? 'Cause I can hook you up with that shit…
Giant squid!
…Logistics TBD.
The problem is they just don’t give a damn.
A particular six-year old boy. . .
Sorry. You caught me in fantasy world for a minute.
A gecko. We get them, but they are always running away. It would be cool to have one to keep on your shoulder as you run errands.
Plus they eat lots of mosquitos just in case someone decides to visit.
One of the horned chameleons.
A King Cobra. How cool would it be to walk around wearing one of those like a neck wrap?
I’d probably have a moose, a great, big bull moose! He’d be an awesome pet that you could also ride. I love their soft, velvety noses and what a view from up on his back 
Polar bear. I would keep him in my parlor making him a …
(We have a plush one on the mantle but a real one would be cooler)
A capybara.