I think things would be more compicated

Well seeing as the only one who would attempt such a thing is a mad man. Yes it would get complicated. I know if I had a time machine I would find out who was on the grassy knoll, give Poland superpowers and turn George Washington into an apple.

I am a huge a huge fan of the short story "A Sound of Thunder" by Ray Bradbury. So, while I would like to say that it would complicate things, I can't help but feel that if you went back far enough and were to stop something (whether that be the big bang or god) that created the universe that the universe would cease to exist. However, this creates a paradox. If you could travel back in time and stop the creation of the universe, you wouldn't be alive in the 'future' to go back in time and stop the creation of the universe. Which would, of course, mean that you would still exsist...And so on and so forth... Although, parallel universes could always prove to be a way around this. You would just 'create' parallel universes where every possible outcome would come into creation. But if you think about this, you didn't destroy the universe, but actually created more. So, you just sort of screwed up all of your plans (if it you planned) to go back and stop the creation of the universe, because you would still be alive in some of these parallel universes.

I have seen a paper treating this question by applying quantum mechanics to it. It turns out that, no there would not be a paradox, and things would not get complicated ... except for the time traveller. This is what happens: You invent a time machine and intend to go back in time to kill your grandfather so you can never be born. You go back in time and attempt the feat. The rules of quantum mechanics mean that since you are alive, the probability that you succeeed in killing your actual paternal grandfather is zero, so the probability of you failing becomes artificially high. It will appears as if the universe conspires against you in order to stop you. Suppose you hold a gun to his head then the perhaps gun would jam, suppose you tried to run him over: maybe an engine would fall off a plane onto your car, killing you. To an observer at the time, everything is normal, everything happened with the probability it would have done otherwise. The plane engine falling off truely can be traced back to a fault in the design of the cotter pin and some bad maintanence. We all have free will, but to the time traveller, it all appears predetermined and there is NO contradiction !... quantum mechanically at least.

I think if you changed anything in the past, all you would succeed in doing is shifting yourself into an alternate timeline, from which you may never return.