No, not the kind of race where you speed to the finish line and win a shiny bauble. Races, as in types of beings in your world.
There are a lot in fantasy that are considered "Old School", such as:
Elves: Beings of fair skin and temperament. Ageless, graceful beings who usually dwell in the forests. They are masters of magical craftsmanship from weapons to clothing. Speakers to and for trees and animals, they're the most mystical in fantasy.
Dwarves: Short, stocky men (for you rarely see the women!) who dwell beneath mountains. Delvers and spelunkers, they dig to the core of the earth to find precious gems and minerals. Their handiwork rivals the elves in creation.
Ogres: Large brutes, somewhat more intelligent than their Troll cousins, they live for war. They can do some serious damage to their enemies, if not rip them apart completely.
Humans: Well, we know about humans, don't we?
Goblins: Short, chittering, greedy little buggers who tend to get underfoot. They reproduce quickly and can usually overwhelm an army just in sheer numbers rather than any sort of skill. They prefer to attack the weak of any given species and travel in large packs.
Drow: Dark Elves. With almost jet black skin and white hair, they are the exact opposites of their woodland kin. Eyes as red as blood and underground dwellers, the Drow have lots of different qualities and stories of how they came to be. Warring with their Elven brethren, they went underground and got involved in arcane magics. (At least according to Dungeons and Dragons)
Of course, in all of this, you can't forget dragons. They are just as important as the others, but I covered them in my "D" post.
There are lots of fantasy creatures that are not "Old School" coming into play more and more these days. There is nothing wrong with creating your own beings as long as you make them believable, for one, and know their creation background, for another.
Be creative! Don't hijack someone else's ideas unless you have explicit permission to do so. The imagination is a powerful tool when used correctly, so think about things in our own fairytales and folklore and expand upon it.