So you've decided to write a time-travel movie. Congratulations! Now you can look forward to all manner of story discussions about causality, paradox and other wonderful issues that will confuse the hell out of your audience if they don't make sense, and probably will confuse them even more when they do make sense.
The very first question you should ask yourself if time-travel is part of your idea is: "Am I dealing with a 'closed loop' theory of time-travel or a 'multiple timeline theory?'" Confused yet? Hold on, we'll take it piece-by-piece.
Closed loop time-travel is the easiest to explain. Essentially what it means is that your characters can't change history because there is only ONE timeline. Even if they go into the past to change things, those "changes are already accounted for in the history they left. In a closed loop, when one enters the past, they aren't changing history, they're fulfilling it.
The first Terminator movie is an excellent example of a closed loop. In an attempt to alter history, Skynet sends a Terminator back in time to kill John Conner, the future leader of the resistance against them. To do so, they actually send their machine after his mother Sarah before she becomes pregnant, the theory being if she dies, John won't be born. However, the Resistance sends back their own fighter to protect her, a man named Reese. Though he dies fighting the Terminator, he eventually preserves her life - but not before sleeping with her. At the end of the movie, Sarah is pregnant with Reese's child, the baby who will become John Conner.
See the closed loop? If the Terminator hadn't come back, than Reese wouldn't have come back and fathered John. Thus, the Terminator couldn't have ever succeeded in its mission because the mere fact that John's birth - a conception that the Terminator attack is a catalyst for - is a part of the future it left means that those events are set in stone. The Terminator could no more kill Sarah and alter its own past than Hitler could suddenly win World War II and immediately alter the history we know.
Another movie that plays well with this theory of time travel is Bill & Ted's Excellent Adventure, when the titular characters realize that their future selves can get them out of present jams so long as they remember to come back in time and make certain things possible for them.
When working with time travel it is essential that you lay down your rules at the earliest stages of plotting. I've read some scripts that start off with clear evidence of the closed loop theory, only to have the characters suddenly able to rewrite history in the third act.
One of my current scripts deals with characters who think they're dealing with a closed loop sort of time travel, only to have the events of the movie reveal the timeline is more malleable. It's been a tricky one to plot because I have to make sure all the evidence lines up the right way without any inconsistency by the end. It's a tricky thing to plot because I have to make sure that the characters' misunderstanding makes sense. The evidence all needs to track in the end, and I need to make sure that all the misinterpretations can be explained away.
On Wednesday, we'll discuss examples where the future is mutable. Bring your Advil. I feel a headache coming on.