There already are. They're racial abilities.
Anything else doesn't really make sense. Oh, Altmer don't know how to cast a fireball? Redguards can't use shield spells? See what I mean?
Anything that basic would be pretty lame. If they added NEW stuff just for other races it wouldn't be so bad.
I could see Th'um for Nords and perhaps a few NEW unique frost/ice spells.
An expanded Beast Talk kind of thing for Wood Elves, perhaps calling for an animal friend to come, generated relevant to the surrounding landscape.
New summons for the Dunmer
New summons or mysticism spells for Orcs, perhaps an actually effective version of Berserk
Altmer could get special NEW versions of Destruction spells or perhaps Restoration
Argonians could get some sort of special Alchemy bonus
Reguards could get some sort of new spells to bolster their fighting abilities...though they don't really need it with Adrenaline Rush being so potent
Khajit could get new Alteration or perhaps Illusion spells
Imperial could likewise get Alteration/Illusion to boost their fast talking.
Perhaps have such NEW spells only develop for PCs of the given race and with a given level of...skill in the relevant skills.
Would give people a reason to play multiple times with different races and different specializations.