Why are dogs and cats the most popular pets?

I think there are several factors here, apart from long established custom. Dogs in particular are very intelligent and sociable, and they make for a rewarding companion. Also, they are easy to feed and look after, and seem to adapt well to family life. Other pets, such as fish, hamsters and rabbits are more to be looked at than really to really interact with.

I think one of the most important points is life span. A well cared for dog or cat can live to a ripe old age, barring accidents, so you have a long time together to build up memories and get to know each other.