Well, any animal we've trained for use would have to be considered here. Oxen, horses, camels, mules, cattle, or really any type of pack/work animal. None of these animals pulled directly from the wild would have performed as needed, and thus had to be domesticated, in a sense, in order for them to be as useful to humans as they were.

Chinchillas have become domesticated. In fact there aren't very many left in the wild any more, but there are tons sold as pets. They were captured and bred for their fur and then as they became more accustomed to human interaction were sold as pets. Also consider pigs. Pigs have more intelligence than dogs, can be kept as wonderful pets, or kept on a farm for food. They all originated from wild boars. Ferrets are another example. Only the black footed ferret, and cousins of ferrets (weasels etc) are wild and yet we have them so common they can be bought at a pet store. There are many animals that we have around us as pets, farm animals, service animals... that have been domesticated to varying degrees from their wild counterparts.

Tons of animal species have been domesticated. Dogs and cats may be the ones you most commonly encounter, but don't forget about cattle, horses, honeybees, reindeer, koi, chickens and sheep.

It is not always clear that an animal was "chosen" for domestication. It might have been deliberate, or it might have just happened. For that matter, you might as well consider the human louse to be a domesticated animal (although it gives us no benefit).

Some interesting questions are:

1. What all animals have been domesticated at some point?
2. Have their been unsuccessful attempts to domesticate certain animals?
3. Are there animals which have been domesticated in the past, but are currently considered as undomesticated/wild?

I think you might be thinking of domestication in the wrong way. You talk about ancient humans "choosing" the wolf as an animal they wished to domesticate. In reality, however, the process was probably both unintentional (the humans didn't know that they were domesticating the wolves, it just happened), and also mutual (the wolves were okay with being domesticated). The actual process probably played out something like this:

A pack of wolves and a tribe of humans would start working together. There was no real decision to do so (by either side), but the humans realized that by following wolves around, they got access to the leftovers from whenever the wolves made a kill. The wolves did the same thing for the humans, for the same reason. Over a long period of time, the wolf pack and the human tribe started to become allies. They got used to each other's presence, and started to rely on each other for things like hunting (e.g., a pack of wolves might find a herd of bison that they can't kill, but humans - with their spears and fire - could. So they lead a friendly human tribe to the herd, and then split the kill with them). Only after we had a steady working relationship going did humans actually start raising the wolves themselves, or even being near them - I think we would have mostly cooperated from afar up until then.

So it's not really a case of what animals did humans choose to domesticate, at least not in the beginning. It was more a case of what animals did humans get along with. Other domestic animals could be domesticated by this process as well - sheep, for instance, could gain protection from predators in exchange for wool, dairy, and meat.

As far as obscure domestic animals go, I know of only two, and both were the result of Soviet experiments in animal psychology. The first was the fox, and it was a huge success - you can buy pet foxes online today. The second was the moose, and it was mostly a failure - moose are too aggressive, too intelligent, and unlike horses, cannot subsist on hay or grass alone.