This is a good article about a woman who keeps rats as pets.
We used to volunteer at the Seattle Animal Shelter, so we used to see quite a few rats (along with hamsters, guinea pigs, rabbits etc). The rats we saw were very interactive, clean, and cool little critters. I suppose hamsters are objectively a little cuter. But, rats are a lot more social. I suppose they are more dog-like whereas a hamster is more like a cat. I suppose that's why hamsters often eat each other if they are in the same cage (now how cute is that!).
Rats are generally seen as filthy carriers of disease. But, As the article says:
...the domesticated rats that are bred as pets are about as different from a wild rat as a golden retriever is from a wolf, said Sharon Jansa, a biologist, rodent expert and curator of mammals at the Bell Museum.
Unless, of course, you're this rat.