This is something that's been bothering me for some time.
It just bugs me when time-travel stories feature alternate timelines where things are present that just shouldn't be given the scope of changes that have been made. Specifically, people who were born after a history-altering event occurs should not be born. The larger the scale of the event, the less likely people born after it are to come into existence.
Say you go back in time and save Archduke Franz Ferdinand from assassination, trying to stop WWI from happening, and by extension Hitler and WWII. Now, events to which history was already rolling may still happen: Ferdinand's death was the spark that lit the European powder keg, but without the event, there'd still be a lot of very tense Europeans waiting for an excuse to go to war. It wouldn't go down exactly as it did in our timeline, and it may have different results, but it would probably happen in some form. (Plus our hypothetical time traveler should just know better that you can change anything in history except Hitler, but I digress :P)
However (and I'm quoting myself from a TV Tropes Wiki article), such an event (or lack of event) would disrupt the actions of pretty much everyone in the world as they reacted to it (or failed to react to it); after that point, practically no couple would have intercourse at the exact same moment they did in "our" timeline, so different eggs would be fertilized with different spermatozoa, leading to a completely different global population after the then-current generation is gone. There'd still be a Hitler, a Churchill, a Roosevelt, a Stalin, and so on, who would live very different lives... but there'd be no Bush, no Blair, no Kim Jong-Il (hmm, I'm liking this new timeline already...), and no hypothetical time traveler.
The most famous example I can think of is Back to the Future. The change to history is relatively small, but it still had a huge impact on George and Lorraine McFly's lives. There's no way they'd have sex at the exact same moment they did in the unchanged timeline, so neither Marty nor his siblings would be born. Instead, the McFlys would have a completely different set of offspring. They might name one Marty, but he'd have different genes from "our" Marty and a different upbringing.
So really, what should have happened for Marty is this: Marty goes back to the future, where there's a different Marty McFly (played by Eric Stoltz) and no one recognizes him, unless they happen to remember "Calvin Klein" from that one week 30 years ago. Doc Brown will have known of the alternate Marty and realized that he's not the same Marty he met in 1955, so he'll just keep waiting for "our" Marty to arrive in 1985. (He'd also probably also avoid stealing plutonium from those Libyan terrorists altogether, and the design for his time machine may be dramatically different.)
At this point, the only thing Marty can do while hoping for anything close to the original timeline he wants is to go back to 1955 again, catch himself before he interacts with anyone or anything (hopefully not causing the universe to implode in the process), and with his doppelganger go back ahead to 1985 to save Doc before he's gunned down. Unfortunately for him, stopping his past self from going back in time will erase both him and the Marty he intercepted from existence (oh, and his dad's still a loser and the happy and successful Stoltz-Marty from the new timeline is wiped, too), but at least Doc ain't dead.
All this hassle could be avoided if the DeLorean had some means of "jumping tracks" between different timelines so he gets back to "his" 1985 without a hitch (and the flux capacitor can't do that... yet), but that means Doc dies all the same.
There are probably a whole slew of paradoxes that I'm not even considering here, but that's why you shouldn't ponder time travel so early in the morning.