Breton - Templar
Redguard - Night Blade
Orc - Dragon Knight
Bosmer - Night Blade
Khajiit - Night Blade
Altmer - Sorcerer
Dunmer - Dragon Knight
Nord - Dragon Knight
Argonian - Templar
Imperial - Dragon Knight
Races aren't meant for classes but for magicka or stamina focus, some are not but obviously some are distinctly better than others.
Magicka:
Breton
Altmer - Elemental damage bonus, so DK's a good choice.
Stamina:
Imperial - Melee restores health, so melee you will use.
Redguard - Melee restores stamina so melee you will use.
Bosmer
Orc - Extra Melee damage so guess what you will want to use.
Khajiit - extra Weapon crit makes for particularly good Stam NBs
Special:
Nords - Health bonus and damage reduction, good for tanks, or any class if you want a little extra surviveability
Dunmer - get a split between Stam and Magicka, with a little more max magicka and a bonus to fire damage - excellent DKs
Argonian - Hahaha, why would you do this?

This is why I always choose Dunmer in case I want to switch between stamina or magicka play styles, it doesn't hurt my dps as much. Dunmer are like the jack of all trades race. They may not be the absolute best in either but they still do pretty good.
Breton - Templar
Redguard - Night Blade
Orc - Dragon Knight
Bosmer - Night Blade
Khajiit - Night Blade
Altmer - Sorcerer
Dunmer - Dragon Knight
Nord - Dragon Knight
Argonian - Templar
Imperial - Dragon Knight
I think Bretons are more sorcs than temps, although the cinematic shows a NB (with a bow)