The time travel paradox has been an interesting subject for many a TV series, from the Twilight Zone to the Simpsons. I personally believe you wouldn't exist because there is already a 'you' in the parallel universe and there can't be two 'you's' in the same place.

Obviously, this is a debatable topic with no definitive answer. Here's my theory on time travel, which coincidentally is not unlike the movie 12 monkeys, which is part of the reason why I like it so much. . Basically, no matter what you do while time travelling, time has already accounted for it. So even though I haven't travelled through time yet, if tomorrow I do and go back in time to change something, even though I might THINK I changed something, it had already happened without me knowing it. If I were to try and kill someone then my attempt would fail, unless that person was meant to die on that particular day. . If anything changes in time, no one of us would have any idea. Think along these lines. I travel in time to kill Hitler before WWII. For the sake of argument, assume I'm successful. Well when I'm eventually born and go to school there would be no reason for me to learn about Hitler never making me want to go back in time and kill him. . If time travel ever becomes possible, there is nothing to worry about only because time has already happened and has taken into account any future actions that may happen in the past.

I really like this question!! So, after pondering this idea, I think essentially you and the parallel universe version of you would switch places. One theory about parallel universes basically says that for every decision made a parallel universe splits off making the opposite choice; so there is an infinite amount of parallel universes containing all possible realities. If you went back in time to get on a train that you had previously missed, you would then be in the reality where you got on the train, but the reality that you didn't get on the train still exists and so another "you" exists there, too.