The second example is that a person goes back in time, without resetting their memory, in order to change events. Twelve Monkeys, Terminator and the Prisoner of Azkaban are examples of this kind of story. There are several ways this can work. The effort can be futile, or successful. The outcome can be mutable or fated. Occasionally the time travel is accidental and the challenge is not to change events (Back to the Future, City on the Edge of Forever).
Here is a site about time travel and movies (gacked from archbishopm's links page ).
Here is a blog all about free will, which has a discussion about the time loop in Azkaban.
I think there are a variety of hypotheses about the nature of time, any of which are acceptable in a story, so long as it is applied consistently. We can believe that there is only one immutable timeline, and what has been will always be. In that case, if we go back in time, then we always have. The past always contained us, and the actions which we 'are yet to take' have already taken place. Azkaban's plotline is at least consistent with this view.
Alternatively, we can believe there is only one timeline, but that we can damage (or heal) it by our clumsy intervention. Terminator is an example of this.
Or we can believe, as I do, that there are large-to-infinite numbers of branching universes, and that time travel just shuffles us about within those, destroying nothing. Are there any films or TV series which represent this effect? Can't think of any just now.
