I've always imagined that traveling in time would be much the same as traveling spacially. Each possible event that could ever potentially happen, being like an infinite number of paths that we choose. Those choices shape reality itself and each persons life is like a few steps down that path.
If we use that as the base concept we could say that if someone could freely travel backward through time, they would be back tracking through the path that was chosen. Once you went back you could effect which path someone origionally chose thus changing destiny. Let's say you go back and meet Adolf Hitler as a young boy of age 6. You spend quality time with him and teach him the ways of Gandi. When you return to the present and start asking about some guy named Hitler or the Jewish holocaust, no one would know what you were talking about. The question though is where did the origional path(or time line) go? I believe that there are not only paths but two states that those paths can be in. The path not chosen always exists but remains in a passive(or potential) state. The path that is chosen is in the active(or actual) state that we are experiencing now. If there is more that one reality, it would most likely be due to there being multiple paths in an active state but that's a whole nother theory.
Moving freely foward in time would be like traveling farther ahead down the "active state" or AS path to the future but it would be a future without you in it. Let's say I want to know what my future holds in 15 years, so I travel forward an arrive in the future only to find that I have no place in it. I do some research to find out what happened an all I would find would be a 15 year old missing persons report saying that I was presumed dead. The problem would be that just like spacial location, if I'm not there I'm...not there. If I step outside of the normal flow of time, I can't interact or interfere with the events that take place in my absence. A person therefore could never know there own future unless someone else did the traveling, saw my future self and reported back to me what they saw. Either that or they could bring my future self back to the present for me to talk to but doing so would alter the future that my future self came from. By this time there would be four of me. My present self, my displaced future self, the new future self that I would become in the alternate future and the much older first future self who decided to stay in the present and prevent me from making the mistakes I would have. Now after that, things get a little....tricky.