I seem to remember Bart in 'The Simpsons' was once asked this supposed Buddhist conundrum. He proceeded to do it...ie rapidly flapping the fingers of one hand against its palm/ thumb-base. Try it. It makes a sound remarkably like the sound of two hands clapping! Ok, you obviously can't get the same volume, but the sound is unmistakeably there. Mystery solved.
It is a Zen-Buddhist question, one answer is that even though one hand is individual, it still needs another one to clap and is incomplete without the other.
Several other answers here:
http://www.angelfire.com/md2/timewarp/sound.html