Combat: Nord, Redguard and Orc.
Magic: Breton and Altmer.
Stealth: Khajiit and Bosmer.
Balanced (can do a bit of anything): Dunmer, Imperial and Argonian.
Good general answer for the starting character. Mostly the differences tend to fade as you level up.
Also, there are differences by gender which affect those lists. For instance, a female Orc might also be considered for a magic user, because of their reasonably high willpower and intelligence (not a bad choice for a battlemage.) And Argonian females are more suited for magic, while the males are more suited for stealth.
In the long run, Bretons and Orcs may be the strongest choices for any type of character, because of their magic resistance.