This is a very important question. The demand for pets determines the supply. Many people can see the use of keeping cattle: they serve as food for people. But what use are pets? The most common reasons for keeping pets are:

• company
• socializing
• they are beautiful, nice and interesting
• status
• something to do

Company
Many people have pets to substitute relationships with partners, children or family members. Many elderly people for instance, like having a dog instead of being all alone at home. This is usually a lap dog, very affectionate and strokable.
The animal serves people's need to cherish, love and fight boredom. But this is really a distressing reason for keeping a pet. The animal is a replacement for normal human contact, something that apparently is too much to summon in our individualistic society. Their pet keeps them from pining. But of course, it has to be a type of dog that suits them and that has been bred especially for their needs.

Socializing
Pets make socializing with others easier. People are more inclined to start a conversation when they can focus their attention on the animal in a moment of silence. Just like with any other hobby, it's nice to talk to people that have the same hobby.

Links inside Animal Freedom:

Bad arguments for keeping pets