Pigs. Porpoises.
Geese are decent guard animals, no? Not so much on fearsome, but they do raise the alarm properly, no?
But dont’cha know? Pig and elephant DNA just don’t mix 
Let’s breed bears. Little ones. They’re closest to dogs and cats evolutionarily, aren’t they?
Rats.
Not only are rats personable and easily trainable, they’re already domesticated. We didn’t really mean to domesticate them, but I’ve read opinions that they should count as domesticated anyway.
Plus they can save lives.
Not such a great idea. Bears are nowhere near the fearsome aggressive creatures they are commonly portrayed, and for non-pack animals they have an amazing tolerance for benevolent interaction with other species (including humans) but they are not particularly amenable to domestication or extended social behavior. Procyon (the common raccoon and Ring-tailed “Cat”) are likely substitutes, as are many rodents (especially the brown rat, Rattus norvegicus) and the various sub-breeds of domestic pig, which in fact already make good pets.
Stranger
I’ve always thought skunks, especially baby skunks, are cute. Of course they’d have to be descented. But on the other hand, anyone who DIDN’T descent his skunk would pay for it. And we could pass laws that require vets to desex skunks when they descent them, unless the skunk owner has a breeding permit.
Bushbabies.
Miniature Pigs
Yeah, skunks can actually make pretty good pets. My mom owned a pet shop when I was a kid, and I had the opportunity to get to know animals of all kinds. Mustelids are another likely candidate, plus maybe raccoons.
Cockroaches. The only problem is that, although they are plentiful, they are very shy and run away at first sight of a human. But maybe if we don’t have a pest spray can in our hand???
I’ve always wanted a pet squirrel. Always. They’re cute as hell (if obnoxious). I know nothing of squirrel behaviours, though - perhaps they wouldn’t make good pets.
There’s a rodent critter in Tanzania called the Rock Hyrax that I’d make into a pet in a second. Again, cute as all hell. But again, no idea about their temperament.
I had a friend that had a raccoon as a pet years ago… Found a starving cub and raised it. From his descriptions, it was a very loving creature, and quite playful. It was much more prone to biting than a dog, but I bet a few dozen generations of selective breeding would clear most of that up.
One of my daughter’s friends had a “pet” squirrel. I put that in quotation marks because the squirrel was in no way domesticated. It was kept in a nice large cage, with hidey holes and toys. However, the squirrel was a very nervous critter, and would startle and shy from humans. I don’t know if they got it as an adult, or if it had been treated badly by humans, or what. But this squirrel was not a good pet. It was cute, though.
Family Canidae & Family Felidae are the only creatures who die. Bears are family Ursidae.
For the reason below…
If they turn on you with your own guns, just remember that Eddie Izzard warned you not to teach them to kick in your doors.
I have had rats, and they are intelligent, playful, and loving. Birds are also great pets…the bigger ones, not the pea-brained finch types. Crows have a nasty sense of humor, and love to play tricks. Hedgehogs are great, as are rabbits and guinea pigs. Why, yes, my husband has outlawed any more animals in the house.
Oh, a tough guy. You got something you wanna say, tough guy? Huh? Well, I’m right here if you wanna say something, tough guy.
In other suggestions:
Bassariscus astutas: Shaw Communications
Suricata suricata: Meerkat Photos, Meerkat Images, Nature Wildlife Pictures | NaturePhoto
Genetta genetta: http://www.juliesjungle.com/genet.php
Lutra canadensis: File:River Otter at the National Zoo.jpg - Wikimedia Commons
Chlamyphorus truncatus: Pink Fairy Armadillo - Land Mammal - Ground Mammals
Tell that to Timothy Treadwell.
Furries 
I also had a “pet” squirrel some years back, but it was wild. I started leaving food on the window sill and later tempted it inside.
Eventually it would run up to me outside, when I was coming or going from home, climb right up my leg, and root around for food in my shirt pocket. I impresed many neighbors and friends.
My friend raised a couple of raccoons. They were adorable for the first year, but then they turned wild… started getting nasty and eventually wandered off.