Fossil evidence suggests that dogs also domesticated themselves, at least at first. They were compared to "party crashers who never left" by Stephan Budiansky, author of The Truth About Dogs. People started selectively breeding dogs a lot sooner than they did cats, but at first they were just perpetually juvenile wolves who followed hunting tribes around and ate their scraps long before humans started using them for anything.
I suppose rats fall into the same category. They've followed humans around the world as well, but only very recently became pets.