I think that the only reason for such popularity of cats and dogs is tradition. At the time when animals were considered mere tools for the human, a use was found for cats and dogs as well. Dogs were bred from wolves, who are naturally living in a pack and are territorial about their living place, so they were suitable for guarding the house and hunting. Cats weren't as friendly, but they natural pray were rodents so they were useful to keep around. While we progressed somewhat from this way of thinking, it's still rooted deeply in most of our upbringings, and only some of us manage to think outside of it (I'm not necessarily counting myself here). Some animals might be more suitable as companions for humans. If we talk about age, turtles, tortoises and parrots live a lot longer than cats and dogs, for example. It was also proven to me that parrots can be very friendly and cuddly. If we talk about intelligence, pigs are smarter, maybe even mice and rats. I'm sure they can be cuddly as well. There are dwarf rabbits, hamsters and similar critters who are also very cuddly.
