Time travel isn’t usually handled very well, especially the paradox aspects of it. If you’ll allow TV shows as well, here’s a list of interesting ones:
1.) Demon with a Glass Hand Episode of the original Outer Limits TV show, written by Harlan Ellison. It’s my all-time favorite episode of a science fiction TV show. Robert Culp stars as Trent, a Time Traveler with missing memories who has been projected back to the present day. He has a computer in the form of one of his hands which tells him things, but is missing three memory modules (three fingers), which it needs to tell him everything. It turns out that he’s been sent because Earth in the future is being invaded by the alien Kyben, who discovered that humans have made the Earth uninhabitable for several centuries, and gone into hiding. The Hand is the only one who knows where they all are – or it would, if it had the other three fingers. The Kyben have them, and have pursued Trent into the past to find out. Wonderfully weird adventure with a solemn twist at the end.
2.) Soldier – another Ellison Outer Limits script, based on his 1950s short story of the same name. Michael Ansara plays a soldier from the future, sent back by an accidental confluence of energies, to the present day. Some great ideas, filmed on a low budget.
3.) The Terminator – I was blown away by James Cameron’s solo directoral debut, which turned out to be not the shootfest I’d expected, but a well-plotted literate piece of genre-aware science fiction. Yes, he was influenced by Harlan Ellison’s two Outer Limits scripts, but it’s not a rip-off (and you could make a case for more direct lifting from Philip K. Dick’s “Second Variety”). It’s darkly comic, and does a lot on a low budget.
4.) Terminator 2 – shows what you can do with a LOT more money. It dilutes the purity and impac t of the first Terminator movie, and gets more maudlin at the end, but it’s still a great flick. See the extended cut, if you can, with the cut “head operation” scene that actually adds something to the film. I didn’t care for any of the further, non-Cameron sequels.
4.) Timescape (AKA Grand Tour: Disaster in Time – interesting and not-well-known film based on Catherine L. Moore’s excellent story Vintage Season, but with a much happier ending.
5.) I agree that Source Code is an excellent film, but it’s a weird one to try to pigeonhole. It’s sortas kinda time travel, but plays fast and loose with time.
6.) The Back to the Future series – some very clever stuff in the films, and cute special effects work.
7.) Sound of Thunder – with some reservations. It’s not really great, and it does weird stuff with the Ray Bradbury novel it’s based on, but it’s a kinda fun film from Peter Hyams. One of these days I’d like to see someone film L. Sprague de Camp’s A Gun for Dinosaur, his answer to Bradbury’s story.
Ones I didn’t like:
Primer
The Time Machine (any bersion. Nobody seems to get what Wells was really saying, or to put it on film)
12 Monkeys (heresy, I know. I’m not really a big fan of La Jetee, either.
Donny Darko
Milennium
Time Bandits
The Time Travelers – 1960s time-travel flick with a cameo by Forrest J. Ackerman. But not particularly smart.
Beyond the Time Barrier – low-budget 1960s flick about a pilot who flies faster than not merely the sound barrier, but the Time barrier, and ends up in a post-apocalyptic world. Pretty dumb.
The Man Who Never Was – Outer Limits Episode starring Martian Landau, who comes back from the future to warn us about its awfulness. Disappointing.
Most of the time-travel episodes of The Twilight Zone