(Story by Arthur C. Clarke and Stanley Kubrick.)
This is the quintessential science-fiction film. It has one of the most accurate portrayals of how space travel is likely to be for us (slow and tedious), and with a lot of attention to detail. And it has the computer that every science fiction film, since, has blatantly ripped off, and usually very badly: HAL (a self aware, artificially intelligent computer; with a dead calm voice virging on the psychopathic, sounding like he's on valium; who's the on-board computer system for the “Discovery” space craft).
The story starts out with dawn of man, where some (unseen) aliens deposit a black monolith, and nudge pre-nethanderthal man into becoming more intelligent. Then with an incredible abrubt change, jumps to 2001. A black monolith has just been found deliberately buried under the surface of the moon, conclusively proving that man is not alone (a more disturbing thought back when it was written, in the 1960s, than now).
The monolith sends a radio signal towards Jupiter (Saturn, in the book, but the special effects team couldn't make a nice enough looking Saturn), and they send an expedition to investigate who, or what, it signalled. Along the way, something goes wrong, and HAL becomes psychotic.
It's a long film (over two hours, depending on which version), with Stanley Kubrick's distinctive cinematography. Originally it was panned as being too wierd, or boring, though it became a cult film.