I think it comes down to what some have already said here, Dog and Cats can be the most domesticated animals. They can be trained to adapt to living in a home among people. They can even become parts of the family. Yes, these can also be said of birds and fish, which are also well known pets in homes. But these don't give the affection to people that dogs and cats do. If your alone and feeling like you have no one to turn to a pet such as a dog or cat will help fill that void in your life.
Also, the life span of the two is good as oppose to some other types of pet. At one time in my home we had hamsters, these are sweet adorable animals, but the problem is they don't have long life span. The average hamster will live only a few years, so we got to the point where we just decided that having such a pet wasn't a good idea.