Actually, it's impossible to
asphyxiate yourself by just holding your
breath. Assuming you had the mental
willpower to do it to the point of
hypoxia, your brain would eventually prioritize low-level
biological functions over remaining
conscious, and you would pass out.
Once that happened, your brain would sense the urgent need for oxygen, and cause you to begin breathing again. And what with you being unconscious, there wouldn't be much you could do to stop it.
So in conclusion, if you're going to commit suicide, holding your breath is not the way to do it.