You know, everyone's mentioning their use in folklore, fables, cartoons, stories, and the like, but no one's really mentioned that the fact that these animals are used so frequently in that type of storytelling is an indication that people almost universally have some degree of reverence (if you will) for those animals. You know... the societies that formed in North America where there were wolves gained a huge respect for wolves, the societies in the desert gained a huge respect for coyotes or jackals, everyone everywhere has been tickled throughout history by how clever foxes seem to act (it seems like almost every culture on the planet has fox fables, assuming they know what foxes are), and so on. You could almost make the case that there's just something fundamentally human about loving these animals (you know... aside from the whole 'nearly driving wolves to extinction' thing). So the real answer probably merits a more rigorous anthropological response than you could get on these forums. Might even make for an interesting master's thesis, or something, if you think about it. Maybe someone's already looked into it.
I mean, you ask why mostly canines, so you might as well be asking why people have had canine companions long enough to elicit an evolutionary bond between us and them to the point that dogs respond more readily to human contact than chimpanzees. People have loved cats forever, too, but it's pretty common knowledge that with cats there's a lot of love but generally a much more indirect sense of loyalty, and with dogs you get a faithful servant forever who practically pisses himself just to know you're back home. So you know... maybe that's why people usually pick canines or felines. Because we always have. I don't know too many people with coatimundi pets.
Can't say much about dragons. Probably what someone said before; they're badass and can does majicks.