I've finally watched one of the staples of 1980's cinema, Bill & Ted's Excellent Adventure. It definitely represents its era well, back in the days of synthetic pop music, big hair, silly clothes and when suburbia was still considered a normal place to be (i.e. not a repressive hell or insane or a fairy tale).
Amazingly, the time travel is handled very well, i.e. without any paradoxes. At one point, future Bill and Ted run into themselves in the present, but they just provide vague advice that won't fracture the space time continuum. At one point, they are smart enough to realize that after their history report is done, they can intervene on their own past behalf to get through different problems, like going back and stealing keys to the jail and leaving them in a convenient spot at the right time. The movie is even smart enough to set up the lost keys at the beginning, long before they become a plot point. Such intelligence was a pleasant surprise among the general silliness of the story.
Time travel paradox is a pet peeve of mine in films. The first Terminator film did a great job of avoiding paradoxes; the second film didn't have any direct paradoxes but surely Sarah Connor thinks that Judgment Day can be averted. I chalk that up to her craziness. One of the great things about Terminator 3 is that they didn't cave in to the "we can change the future so there is no robot army that sends back the cyborg that we just destroyed" thinking of Ms. Connor. The TV show is awash in paradoxes, so much so that I've lost track. But the show has a certain charm about it. They have a sense of humor if not of consistency.
Having a sense of humor is what also saves the Back to the Future trilogy. It also suffers from paradoxes (if Marty changed his parents' lives then he shouldn't remember their slubbish ways because it never would have happened), but consistently thought out time travel isn't really the point. Plus, the third film is really fantastic. Of course you know Marty is going to make it home, but what about the Doc and the teacher? Christopher Lloyd (the Doc) and Mary Steenbergen (the teacher) have good chemistry and since they are a secondary story line, a happy outcome isn't guaranteed.
A rather unhappy outcome is the movie Primer from 2004. The filmmakers focus on the ideas and schemes of the group of scientists who stumble into creating a time travel device. The characters use it to make money at day trading and try very hard to avoid any paradox by having people run into themselves, etc. But the filmmakers fall into the old trap of wanting to have some big drama and they descend into paradox. The main appeal of the movie is supposed to be how well thought out and serious it is, and in this it fails. They should take a tip from Bill and Ted, lighten up and have an excellent time.