If it was possible to travel into our past, the most you could achieve is to make events occur as they already have occurred. You couldn't go back and prevent JFK from being shot, all you could do would be to accidentally (or deliberately) bring about his shooting. We know he was shot, so he would always get shot (by the same culprit) whatever you were to do. More likely, you just wouldn't be able to interact in any physical way with the universe around you.

Much is made of differing alternate futures, every tiny decision you make generates subtley different alternate realities, and this is often used to explain away the consequences of travelling back in time and affecting events there. While this may be a possibility, this would then trap you into a different time stream where events had always progressed along that different path. You would be unable to change past events and return to the point from which you had started. You would be stuck with a completely different chain of events.

Rather than thinking of history as an ever branching tree, starting from a single root in the past and gradually branching out into ever more and more branches as time goes on, think of it more as a grid of chickenwire. every decision now brances out as time progresses, but also multiple events in the past can combine to generate the future we know as the present. If you were to try to go back into the past and prevent your grandparents from concieving your parents, this would not create a paradox. It would not mean that you didn't exist to go back to stop them meeting, or whatever, as we know that that isn't the case. History would just take an alternative route. If I were to travel from one city to another, I could travel along motorways, main roads, minor roads, even by train and still achieve the same end result (though the road "me"s may have to wait some time for the rail "me" to catch up if I was using the British rail system).