Warrior: Redguard or Orc. I haven't decided yet.
Mage: Breton or Altmer, depending on how powergamey I want to be (In Oblivion I chose Altmer to get the most Magicka possible).
Assassin: Probably Imperial or Argonian, depending on the available guild.
Thief: Khajiit or Bosmer, depending on the overall mood of the game.
Spellsword: Most likely a Dunmer, though I may go Breton just for the Magicka boost.
I refuse to make a Nord in Skyrim, just as I refused to make an Imperial in Oblivion, a Dunmer in Morrowind, and a Breton in Daggerfall (I did make a Redguard, though).