That's a question from The Straight Dope, and they don't give a very satisfying answer (it's basically "I don't know").

But I think the answer is embedded in there anyway, in this part about the tendency of certain mechanisms to be turned clockwise:

To be sure, Morris concedes, there are a lot of clockwise phenomena as well: the direction of the pieces on a Monopoly board; the "on," "higher," or "tighten" direction on knobs, dials, faucets, light bulbs, screws, and bottle caps; dialing on a rotary telephone; record turntables; and turning a manual can opener, eggbeater, or pencil sharpener. But most of these--at least the ones that involve exertion--are easy to explain: most people are right-handed, and righties have more strength turning clockwise than the other way.

The direction of races as being CCW is probably also due to handedness. In chariot races, skating, and to a lesser extent running, the racers have to jockey for position. Since most people are right-handed, it's probably easier to shove or elbow someone with your dominant side. Racing CCW means that the shortest distance is hugging the left side of the track, and using your right arm to jockey for position.

Makes sense, right?