I have a fondness for Tolkienique elves, and elf-like beings. Possibly because they remind me of cats.
I’m torn between Elfquest elves (wolfriders, mostly…I had a slightly embarrassing crush on Skywise for a LONG time), the Draenei from WoW, and the Ogier from the Wheel of Time books.
Though they are actually human, much like a vampire, they change enough to be a sub-set of humanity, and live in a somewhat different plane of our reality.
It is what I always inspied to be if I never grew up.
The Shire 500, sponsored by National Pipeweed.
Or did you mean a different kind of race?
Actually, I always wanted to be a vampire. Too bad I’m not an Emo douchebag, or I could live the dream, almost…
Joe
Hmmmmmmmmmmm - don’t know if they really qualify as a race because they’re technically human, but the Bene Gesserit and Mentats of the Dune universe are pretty damn cool. If I got to choose I’d probably be the former, although there aren’t many career opportunities for Bene Gesserit boys.
I assume you’re asking about sf races, too. Ever since I saw Star Trek’s “Journey to Babel,” I’ve had a thing for Andorians. Blue, strong, warlike, cunning… they’re just so cool! Andorian - Wikipedia
Dragonewts, from RuneQuest’s Glorantha.
Fat little Hobbitses.
Dwarves. Good, strong, sensible folk, and they pervade fantasy literature perhaps even more than elves. And their bread is to die for. 
Leetah was all kinds of fine. And I hear Elfquest the movie is coming out in 2011.
Warhammer Dark Elves put the other evil races to shame in that world; Chaos (PINK horrors, oh the humanity!..though Nurgle is pretty cool), Chaos Dwarfs (a race that wears hats bigger then they are, are you kidding me?), Undead (who almost make it except their war machines are hilarious).
You mean “from”.
Since someone already mentioned the Borribles, I’m going to have to go with the Nac Mac Feegles. Drinking, brawling, cursing wee Scottish fairy-folk. What’s not to love?
Trills. So cool how they get to accumulate lifetimes of experience from so many different perspectives… and the way all of those different influences have to work together within one body. What’s more open-minded than a Trill and its symbiont?
But only a very small portion of the population gets to be joined, and it’s a complete bitch of a process to qualify too. You thought getting into grad school was a hassle - try qualifying for a symbiont!
I’d probably have to go with centaurs, if we’re speaking of how they’re portayed in fantasy. Noble, bold, courageous, wise, strong, and all that.
If we allow science fiction races, I’d have to sit down and think 'er over.
Cubans.
Change bread to beer, and I’m in.
It’s too bad about their womenfolks though…
Nah, Dwarfes kick ass!
They have centaurs in sci-fi, too. At least two different species…the one group from Chalker’s Well of Souls books and the Titanides in Varley’s Gaea books.
Drow–for that marvelous Drowish cheesecake!
Werewolves. Granted, in many fantasy settings lycanthropy is treated as a disease rather than a legitimate race per se. However, this is not too different from the situation in real life, where the psychiatric condition of “clinical lycanthropy” (the delusion that one has the ability to transform into a wolf) has historically been confused with actual, heritable lycanthropy.
In real life, of course, werewolves do not constitute a race, but a synklepton.