Forbidden Planet (1956)

It's easy to smile at Forbidden Planet now, but it was hugely ambitious for its time, and you can see its fingerprints all over later sci-fi. It's essentially Shakespeare's The Tempest in space, complete with a scientist, his daughter, and Robby the Robot. The science is a mixed bag, but the central idea is genuinely clever: an ancient alien civilisation built a machine that could turn thoughts into reality - and it destroyed them, because they forgot about their subconscious. That's a surprisingly thoughtful idea for a 1950s film, and a good warning about technology we don't fully understand.