Dogs are an interesting case. Here's one of the more common theories I've read about their domestication:
Animals have a certain 'personal space' where predators or other threats can be tolerated, because they need to eat. Like zebras, who walk around eating only a couple of meters away from a pack of lions. If the animal is too flighty, it starves. If it's too foolhardy, it'll get eaten. Starvation is generally a bigger issue with pack animals.
Different wolves in a pack would have different personal spaces where they would tolerate humans while they scavenged for food. The more foolhardy ones would survive more often because they would get more food, and early man had better things to do than chase off every scavenger at their camp (and they could escape most of the time anyway). Over a long period of time, these wolves would get used to the presence of humans, and follow them while they were hunting, possibly even assisting them by harrying the animal or distracting it. At some point early man went "These animals could be trained to my benefit!" (and they could), and we end up with what amounts to the precursor of modern dogs. And then we get into selective breeding, which is much more interesting but I'm getting bored and drifting off-topic.
While I'm at it, one of the big reasons Europe was dominant until recent times was its rich soil, especially in the Fertile Crescent. This, combined with a huge amount of viable crops, its wide variety of domestic animals, and the fact that it has a large area of viable land (not having to sail to find new places makes it much easier to advance a civilisation), let them advance the way they did.
Diamond actually points out that Europe only had access to metalworking, philosophy, and almost everything beyond basic survival pretty much solely because of the horse. No other animal is anywhere near as good at work as a horse.