Borneo in fact still has “pygmy” elephants (still run about 8 feet tall), though their numbers are dwindling due to the usual environmental degradation/habitat loss reasons.
If you want to reduce the size of a large species, isolate it on an island and let it breed for multiple generations (like the critters on the Shetland Islands). It’s called insular dwarfism.
That article has a sidebar about the extinct dwarf elephant of Pleistocene Malta and Sicily. Ran about three and a half feet tall.
The pony herd on Assateague/Chincoteague islands are nasty at times. There are signs warning that they kick and bite. And yet people constantly try to get selfies with them and get kicked/bitten.
When I last camped on Assateague, there was a foal that got separated from the herd. It was becoming weak, stumbling along. People kept trying to get the park rangers to do something, but they have/had a strict policy of nonintervention.
They can be helpful with mail delivery, as well 
Storks bring babies😊
Given that the domestication of ferrets has worked out well, I think the pine/American marten might be a really good candidate. The videos I’ve seen of ones raised by humans after begin orphaned are great.
They are, at least, descended from domesticated horses and can be trained to be useful when they are culled from the wild herd.
No thank you. I’ve seen Conquest of the Planet of the Apes.
All ‘wild’ horses, like the Chincoteague Pony, the Mustang, the Australian Brumby, the Camargue Horse of France, and quite a few others, are actually feral domesticated horses, and most are traditionally culled out the the wild herds for training.
The only extant candidate for a true wild horse (not descended from domesticated horses) is the Przewalski’s Horse, known as the Takhi in its native Mongolia. It is not the ancestor of the domesticated horse, but a close relative which diverged from our horse at least 38,000 years ago and possibly much longer.
Horses return to their original lifestyle very easily. A feral band of horses is dangerous like any other wild animals. Stallions attack what they perceive as threats. You would not want that to be you and your stupid selfie camera.
The Tarpan, a wild horse which existed in Europe well into the 19th century, was considered to be untamable. It remains unclear whether it was a feral domesticated horse, a hybrid between the horse and the Takhi, or something else.
And tasty. Yes, I have eaten Hyrax.
Rather like rabbit, more flesh than guinea pig. We girilled it, but I would make a pie if my friend ever illegally shot one again, in a National Park.
Seeing as he is now an adult, that probably will not happen.
True. I was responding to a prior poster who noted the Chincoteague horses had a nasty disposition.
I had not known until today, that new blood has been introduced to the population several times (as the existing herd was suffering from many problems due to inbreeding).
I think porcupines could be domesticated. I have only met two, but they both really, really liked hands-on attention.
Warthogs could feasibly be domesticated. I have direct experience with one. He was in a zoo. My brother and I reached through the fence and scratched his back and tummy. Later that day he escaped his pen and found the two of us. He was adorably interested in MORE scratching.
Unfortunately the zoo-keeper staff were less than keen. But absolutely bizarrely, they, instead of capturing him themselves, chose to ask myself and my brother, probably aged 6 and 8 at the time, to lassoo him. Poor pig.
Anteaters have been tamed. They can be walked on a leash and are at least as smart as dogs, and eat things besides ants.
Capybaras are trusting and cuddly, though like large guinea pigs they don’t display a lot of personality, that’s why capybara videos on YouTube don’t get a lot of hits.
Pirates are aggressive, must be supplied with rum and their habitats are ships, which few potential owners would have the means to provide. Not reccomended.
I’ve known fully domesticated geese who are just general assholes.
And have no compunction about crapping on you while they bite you.
Noisy don’t even explain it *
So careful consideration before domesticating any animal.
*Hey! I have cats like this. Don’t listen to me.
Australian Magpies.
Very smart bird, fearless and agressive, but great memories. In nesting season I’ve sat out the front and thrown food to them, had some ballsy enough to come right up to me and take it out of my hand.
Last spring I watched one trying to get a length of busted fairy light wire out of the tree in the front yard. he’d grab it and fly off only to be yanked back when the wire didn’t break. So I went and got a pair of pliars and slowly walked out to the tree while the Magpie watched me, cut a 3 foot length off the wire, held it up to show the Magpie, dropped it on the ground and slowly walked away. I got 3 feet away before he dropped down, snatched up the wire I’d dropped and flew off to do some nest building.
My Mother had a Myna bird.
It only said one word. A dirty word. (Goddamn)
It usually sounded pretty correct. To us.
We ignored it when others were around, hoping they didn’t notice.
He was a consummate thief. Anything was fair game. Lay a earring, hair tie, a Tylenol tablet any old thing down, he’d swoop in and get it.
As much as I’d like a bird as a friend/pet I think they’re kinda hard to live with. Plus they can’t be potty trained.
Frankly they are famous for this. The Romans kept them as guard animals. And yeah, they can sure set up a ruckus if something sets off their alarm system.
That’s a (popular & persistent) myth, based on a review of direct evidence, as well as my own experiences: bear, bobcat, mountain lion, African lion, fox etc. etc. make excellent fare. But raising meat-eaters for meat doesn’t make economical sense, and the bigger predators are lethal to humans, in a way even raging bulls aren’t.
That being said, dogs were used as “incidental” food over much of human history (prehistoric sites with dog bones with food prep evidence are extremely common & widespread), and in some rare cases actually were raised for food. They are smallish omnivores, which makes the business a little more profitable.
They are relentlessly mellow beasts - they’re prey animals but way too big for most predators in their environment.
My candidate is Pallas cats. They’re like big fluffy Loraxes, and they stand on their own tails to keep their feet warm in the snow.
I’m not sure if it’s already been mentioned but chipmunks seem to be easily tamed. Although I can’t imagine what they’d be good for other than a pet. 
There are also additional reasons to have dogs around – human societies also kept dogs as hunting assistants, protective guardians, warning notices, sometimes warmth sources, and often companions. But having dogs around sans modern veterinary services means excess puppies; no surprise that dogs were often a food source – plus which, of course, they’d all or almost all become an emergency food source if food was really tight, in which circumstances there also wouldn’t be enough to feed them.