She's a blue Russian Dwarf Hamster, and is actually very clean. I clean her cage every 2 weeks but it's rarely ever dirty and never smelly. But every once in a while, if Sprinkles gets scared she'll sprinkle or tinkle on you.
EDIT: Yup, I've had rats before too But I disagree. Rats in my experience are way dirtier, but possibly because it's the size of the rat versus the tiny little dwarf hamster.
Aw my Taz was a blue Russian. He was evil to every living creature except for me because I didn't put up with his shit. Embarrassing picture inbound. Had to take a shot with my phone because my scanner/printer deal isn't here.