Solving the Time Travel Paradox

Time travel has always been my favorite SciFi topic. But it has inherently one main issue, the PARADOX.
A simple version of a paradox (to explain it to those of you who for some strange reason are still reading and yet do not know what a time paradox is) would be, say you travel back in time, and while you were driving around in the car you stole (shame on you), you have an accident and kill a kid, who turns out to be you!!!
Now, the problem is, if you just killed your self when you were a kid,...