Well, my top 5 time travel movies would be:
- Time Cop
- The Time Travelers (from 1964)
- Back to the Future (the trilogy)
- Star Trek IV: The Voyage Home
- Beyond the Time Barrier (1960)
I like
Time Cop because it's just such a well-executed concept. You can do almost anything with time travel but I think this is Jean-Claude van Damme's best performance, and he had a solid supporting cast.
The Time Travelers came at the tail end of the "nuclear war will destroy civilization" era in the movies, but it was largely apolitical and it still holds up well (in my opinion). Some of the characters are corny and stereotyped, but the concept has always impressed me as being well thought-out.
Back to the Future does everything wrong but it's just a fun bunch of movies.
Star Trek IV remains one of the best in the franchise. I think because it just focuses on character - but maybe because it's also as relevant today as it was in the 1980s.
Beyond the Time Barrier is another post-apocalyptic story, but this one has nothing to do with nuclear war. Humanity has been all but wiped out by a devastating plague and the last survivors are struggling to hold off a wave of mutants. Of course, the mutants are a convenient threat and some people would argue that the plague was a metaphor for nuclear war. But the movie's main premise was that if we know we'll create a terrible future for ourselves, then we have a chance to avert it.
Recent events seem to suggest we don't take advantage of advance warnings, though.