Dwarves suck at arcane magic. Haflings make for poor fighters. This is what I call an implied setting, and D&D was developed with one in mind from day one, I believe.
As a DM, you're free to change the implied setting, but that's a big part of what makes D&D being, well... D&D. It was one of the major reasons keeping me away from 4E; the amount of offense to what came before (eladrin? new cosmology? evil paladins?).
That said, the implied setting deserves mechanical support. You can easily house rule racial differences out of your game, if you want to. Creating different races out of nowhere is not that simple.
Cheers,