This is my kind of discussion. I've got a lot of "what if" questions about time travel and paradoxes. Let's get started...
Let's say I'm a JFK assassination historian. I've written several academic papers, a couple of textbooks, and have been on lecture tours. A time traveler from the future goes back in time to 1963 and prevents the assassination of JFK. What happens to my life's work? What happens to my memory of JFK's death and aftermath? What about the millions (billions?) of other people with the same memories of JFK dying on November 22, 1963? What about all the history books, newspapers, news reels, etc. that recorded the assassination? >Poof< They're gone?
Hence the time travel paradox. My vote is if a time traveler could stop the assassination, then you'd have a different vocation since the assassination never happened. Doc Brown understood this: