Domesticated animals have been selectively bred over thousands of years to suit our lifestyles making it mostly a symbiotic relationship, though we gain a lot more than the animals do. Domesticated animals look very different and even have different DNA than their wild counterparts. (This is a good place to mention that you do not, and in most cases should not be the "alpha" to your dog because they're so extremely different from wolves. We don't treat humans like chimpanzees and we share 99% of the same DNA!) That doesn't mean that all domesticated animals make good or practical pets for everyone.
Here is a list of domesticated animals, though some animals are still in the process of domestication.
Just because all of these are technically domesticated animals, how we exploit them for food, milk, fur, skin etc is unethical.
Before you get a pet, make sure you understand their needs, how much space they will need, how expensive and time consuming upkeep will be, and of course where the closest vet that will see this animal is, plus an emergency vet for when your normal vet is closed.
They fall into 3 main groups: companion animals (mainly dogs and cats), farmed animals for food and fur etc (sheep, cows, pigs, poultry, etc.), and working or draft animals (dogs, horses, camels etc), though in my humble opinion, farmed animals and working animals can also make great companions, if the conditions are right.
Man's best friend for centuries and I think the first domesticated animal. It's been said that both dogs and humans could have been extinct if it weren't for this simbiotic relationship.
Before we had houses and electricity, we lived in groups or tribes, hunting and foraging for food. Those tribes with "dogs" had a built in security system to alert them of dangers. The dogs would also eat our scraps keeping our territory clean where tribes without dogs would throw away the parts of animals they couldn't eat which would pile up, mould, smell terrible, grow bacterias and germs and force them to relocate and build again from zero.
Now, we mostly keep dogs as companions. Different breeds bring different elements to our lives so choose your dog wisely. If you're very active or live on a farm where your dog can run free all day, a border collie or other kind of active dog would be ideal, but if you live in an apartment and don't get out as much, a pug or an English bulldog might be a better choice. If you have allergies, there's no dog that's 100% hypoallergenic but there are many dogs that shed considerably less to choose from. Never get a companion on impulse. Do your research and choose a dog based on size, energy level, look up how often they need grooming and check your local groomers pricing, temperament etc and I possible, keep an eye out at shelters for your perfect dog. Dogs can also be trained to be therapy dogs, service dogs and emotional support dogs which can be life savers for people who suffer from anxiety or have disabilities.
Some people think that it's cruel to have a service dog but these dogs get the best lives. Their handlers generally feed them the best foods and make sure they're very well cared for because we need them around for as long as possible. These dogs have a bond with their handlers like no others because we rely on them as much as they rely on us. They also get to spend more time with their handlers (aka, the person they love most in the world) more than other dogs. They also get downtime, playtime and time to just be a dog.
These funny, cute creatures are generally farmed animals but can make great companions too. But they're not for everybody.
At AnimO, we have a small herd so I can speak from experience. Goats are herd animals and need to be with their own kind. Never keep a lone goat or they'll get extremely depressed. You'll need to find a good goat vet that's easily accessible. They eat half their bodyweight in leaves and grasses a day so be prepared to grow your own food for them. Their pee is stinky, so be sure they have ample space and a way to drain the pee and keep them away from neighbors houses. Females will scream bloody murder during mating season if there are no bucks (in tact males) to mate with. In tact males can get quite aggressive if not socialized properly so you need to spend time with them every single day, hand feeding them, holding them and giving belly scratches.
They sound like terrible companions! But I promise, the hard work pays off. They are gentle and sweet if you put the time in. They are cute and playful and a joy to be around. They will weed your entire neighborhood. And did I mention how adorable they are?
I used to ride when I was a kid in England. I think I started at 4 years old and that's when my love for horses began. I'm not very keen on riding horses now since I did a lot of research on them. You should only ride young healthy horses and calculate the weight they can carry without stress. Inexperienced riders can cause damage to a horse's spine so I don't like facilities that offer adults their first horse ride.
The good thing is that you don't have to ride horses, or make them pull carts. You can keep them as companions! They are intelligent, sweet, long lived and form strong bonds with their care givers. But you will need a good vet, frequent hoof care, access to lots of grass and good quality hay and feed, a large paddock, and in Japan, you will also need a contract with the city for poop pickup, even if you opt to use the manure for fertilizer, you still need the contract.