If you were to go back in time and kill the past you, what would happen to your present self?

A couple of friends and myself were a bit under the influence when a popular topic surfaced, time travel. I was wondering what is the theorized belief of what would happen for such an action. As my friend not so eloquently put it, you would disappear because you broke the rules of the universe and that's that. I on the other hand, do not think it would be as simple as the 'Back To The Future' reference. Since you just created a time paradox, what would happen? Opinions will be duly noted and for all intents and purposes of this question, let's pretend that time travel into the past is possible.