Thinking about that is really hard. I mean, what if you'd go back, and stopped yourself from being born. Then what? Then you wouldn't live and wouldn't go back in time either. Would you "vanish"? Or not?
What if you travel back 30 minutes and plant a dynamite? Then you couldn't be planting the dynamite, because the machine was blown (assuming you use a machine, as in Sci-Fi). So travelling back sucks