Joseph at The Grognard's Lawn says some things about character races that I mostly agree with: there should be more variation within individual races, especially within humanity; the nonhuman races are too ridiculously attractive, compared to humans; and turning elves and dwarves from supernatural beings into mere humans with extra bonuses is a real disservice to the spirit of fantasy. But I have a couple comments to make on the topic of races.
First, although D&D elves and dwarves have certainly developed into strongly-Tolkienized fantasy races, the original LBB elves and dwarves had very little Tolkien influence. The Tolkien influence on dwarves is the strongest -- they have beards and axes and the v instead of f; everything else is arguably present in folklore. LBB elves borrow sharp senses from Tolkien. Although Joseph quite rightly points out that most sword & sorcery does not have nonhuman fantasy races, there are a few (Zelazny's Dilvish the Damned was part elvish, Elric is basically an evil elf, Corum is literally called an elf.) And let's not forget that there's a non-S&S fantasy tradition that draws heavily from fairy-tales, Arthurian romance, The Faerie Queen, and so on.
Second, I can't stand defining races as a bonus to an attribute or set of skills. It's flavorless. For human variants, I think the best bet is to create one or two variant talents that a member of that culture can start with, replacing one or two common talents. For example, an exotic desert-dwelling culture that can't start with knowledge of swimming (because of the rarity of large bodies of water,) but which has a "sand-swimming" talent as a replacement. A PC from this culture isn't forbidden from learning swimming, nor are other PCs forbidden from learning sand-swimming; they just start out from different baselines.
For nonhuman variants, give them some truly different abilities that are individually internally balanced, such as dark vision combined with either eerie glowing eyes (visible to enemies in dark, reaction penalty) or light sensitivity (more easily surprised in daylight, attack and skill penalty.) Plus, each nonhuman race could have at least one additional negative feature. Nonhuman races with limits are more interesting than superhumans.