Because dwarves are 100% pure, undiluted awesome.
More seriously, they have many traits seen as very positive to many people: loyal, close with family (clan), strong sense of responsibility, good work ethic, are meticulous with details (both in crafts and planning), they are masters of their craft or field, tremendous mental and physical fortitude, work for the good of their family, community, and race, and they have a strong sense of honor and will stand up for what they believe in, even at potential personal loss.
On the negative side, they tend to be insular, greedy, and distrustful of strangers. Of course a lot of people nowdays share these same three traits to some degree, and being insular and distrustful of strangers CAN be good things as well. There is also a certain appeal to playing a character you can reason that "I'd be like this on a really bad day, and didn't give a damn what anyone thought about it."
Plus, I think there is a certain amount of truth that many gamers can identify with dwarves to some degree- I know of all the non-human races, I can identify with them most strongly. Dwarves in most settings are depicted as the underdogs, fighting against tremendous odds for survival, but they still never give up- and thats a strong theme in a lot of fiction and movies that most people relate to and admire. If I were going to hang out with any group of non-humans, it would definitely be dwarves.
I think other races (such as elves and drow) tend to draw so much hate because they display many characteristics associated with slackers and/or rich/snobby/spoiled celebrities in today's society (think Paris Hilton meets Joe Dirt), and because they were held up as uber-awesome and super cool in previous editions, and were supposed to be held in awe by everyone. The elven attitude of "I'm just superior so get used to it and do what I say because I'm obiviously better" is also extremely annoyong. Finally, many of the elf fanboys are extreme enough to make most people loathe the idea of elves. I know my hatred for elves stems from a combination of these factors.
But on the plus side, I don't see much halfling or gnome hatin' around here (unless we're talking about kender).
