Star Trek (2009)
As the third installment of J.J. Abram's reboot of Star Trek is hitting the big screens, let's recall that in the first one, time travel was a major plot point. Nero blames Spock, in his capacity of ambassador to the Romulans, for the destruction of his planet as a consequence of a Supernova. They confront each other their ships are swallowed into a black hole sending them to the past (albeit 25 years apart from each other). It's time travel in it's simplest incarnation: being back in time Nero tries to possibly prevent, but mainly to revenge the destruction of his planet. History is rewritten. In this case, those involved, such as Spock from the future, do know that things are happening in a different way. The paradox is obvious: in this new history, the Romulans' planet may not be destroyed (so there is no confrontation between Nero and Spock and they don't travel back in time). If you wish to consider that the destruction of the planet was inevitable, then the difference now is that Spock knows he'd be blamed and would do things different, again possibly avoiding the confrontation that ed them to travel back in time. The paradox is still there.
In the movie it is chosen to just let it slide, and it is even made a matter of jokes between the young and old versions of Spock, who meet in this memorable scene:
Our score for Star Trek (2009): 330.0 - do you agree?