This is a question many scientists have tried to answer. Handedness itself is quite an odd phenomenon - most of our nearest relatives, such as chimpanzees, show no preference for one hand over the other (though in certain groups there is a bias, again towards right-handedness). Because of this, it is thought that handedness may be tied to the evolution of language. Speech processing usually takes place on the left side of the brain, which could have something to do with right-handedness - but this is also true of left-handed people.
It is possible that, overall, being right-handed is more advantageous than being left-handed - there is some evidence that left-handers can have more trouble with language, for instance - but that being left-handed can offer an advantage in combat because, to a right-handed opponent, a left-hander is unusual and therefore harder to fight. This could explain why left-handers have survived (handedness is inherited to a certain extent) even if, overall, right-handedness works better. But there is no really conclusive evidence yet.
The handedness research institute could offer you some more help with this question.