My favorite type of character to play, at least in Morrowind (Since I don't consider Oblivion canon in the Elder Scrolls universe) was an Imperial Agent born under the sign of the lady. What's that? 85 personality at level 1? House Hlaalu, here I come.
My favorite race would certainly be the Dunmer, though. I mean, they've got so much going on. Their main religious structure is forcing out the native culture and religion while at the same time feeding the hungry and healing the sick. Their aristocracy is either a bunch of backstabbing, greedy, yet honorable merchants and nobles, another is a house of crusading paladins, and the last are badass wizard lords that live in giant mushrooms, and that's not even the half of it.
Hell. Fucking. Yes.