While we domesticated dogs, cats basically domesticated themselves
Many people know that dogs were one of the first animals to be domesticated by humans. Early in our hunter–gatherer days, it is belived that we pretty much kidnapped wolf cubs and raised and bred them as hunting companions.
What most people don't know is that cats basically domesticated themselves. Once humans had moved from a hunter–gatherer society to a more agrarian one based around growing crops, we inevitably ended up with large stores of grain in warehouses and primative silos.
As any farmer can tell you, when you have a lot of grain in one place, you will invevitablly end up with rats. Because of this high concentration of food in the form of rodents, cats started to evolve to be more accepting of humans and eventually became pets.
We tolerated cats because they kept the rats out of our food, and cats tolerated us because our grain stores were an all you can eat buffet for them.
It's belived that this domestication happened in Mesopotamia and ancient Egypt—and led directly to the worship of cats as gods in those societies.