A great line from a South Park episode:[at the time portal. News vans, reporters and scientists, one in a space suit, gather around and marvel at the portal] Aaron, I'm standing at the time border which scientists say follow Terminator rules. That is, it's one way only and you can't go back. This is in contrast, say, to Back To The Future rules, where back and forth is possible, and of course, Timerider rules, which are just plain silly. Anyway, it appears that the man from the future is here to stay.
First off, I have to say... I don't believe time-travel is possible. Nothing surpasses the cosmic speed limit, c. Worm holes and space-time curvature are wild exaggerations that help describe a theory, but there's no reason to believe it's possible to tear space-time. Still, it's a fun conversation topic for the logical and philisophical implications.
Back to the Future has a memorable scene (oddly one of my wife's favorites) where Marty McFly literally fades transparent as his parents almost don't hook up. Even if the effects were cheesy, it shows the writers relied on a single linear timeline. Apparently, even if Marty from Timeline-A travels back and prevents his own birth thereby erasing Timeline-A, the new Timeline-B would still become a new permanent timeline. A bit of a paradox, but hey it comes with the territory and those were a fun series of movies!
The Terminator movies got a bit more into destiny, and a lot more into paradox. SkyNET and the machines travelled back to kill Sarah Connor, who would give birth to the leader against the machines, John Connor. The trippy part was: John Connor sent Kyle Reese back to save his mom, and Kyle Reese has sex with John's mom becoming John's biological father. So, one must assume... some timeline must have originally caused Kyle Reese to go back and hook up with Sarah Connor for John to have ever existed. Either that, or Sarah Connor had some serious machine-ass-kicking genes... and she birthed a John Connor by another man in an original timeline who led the fight against machines.
Now, there's a whole category of time-travel stories that are pretty ridiculous - the "go back and fix it" premise. Superman: The Movie has one at the end where Superman flies around the Earth (presumeably > c) to save Lois. Star Trek IV has one where they go back to get a humpback whale because a whale-song-loving-alien is threatening Earth. It's amusing that they fly around the Sun (presumeably > c) to travel backwards, then conveniently do the same thing to return to the future. It's all worth it to hear Spock cuss though. I wouldn't call Groundhog Day a time-travel flick... it's more of a deja vu scenario.
Time Cop is probably the worst time-travel movie ever. Not only are the characters going back and interacting with their past selves without altering their memories or the timeline. They switch to 'Back to the Future' rules when the past-villain gets a cut, and the scar appears on the future-villain's face. Then they change the rules again at the end of the movie after Jean-Claude Van Damme's character prevents his past-wife's death. He returns to the future to find he has children with his wife he has no recollection of. If there's one thing that makes a bad time-travel movie, it's inconsistency of applying the rules.
There are so many great time-travel flicks. I haven't even talked about Time Bandits, 12 Monkeys, Butterfly Effect. Then there's more bad ones like Bill & Ted. (How come the 80's were such a big decade for these films though?) The movie I watched tonight, Truecrimes, is worthwhile for anyone who likes time-travel flicks. It had a bit of chicken-egg dilemma in it, but taught the same important lesson as most time-travel movies: Just don't mess with time-travel, it ain't worth the trouble it will cause!