Metropolis, directed by Fritz Lang, 1927
It's arguably the most iconic scifi film of all time. Even film fans who haven't seen it recognize Maria, the robotic protagonist that graces most of the marketing material for the film. Sadly, most cinephiles I know dismiss it. It's slow, silent, and the German expressionism can be a bit disorienting (I personally love it). Metropolis has long been in the public domain, so you can find it pretty much anywhere - youtube, discount DVD bins, etc. Like so many of the greats from the dawn of film, much of the original footage has been lost. In 2008, a cut that is a full 30 minutes longer surfaced in Argentina. I'm dying to see it, but I don't believe it's available just yet.
It tells the story of the titular city, Metropolis, a dystopian mega-society. Much like the Morlocks and the Eloi, the populace of Metropolis is separated by a staggering class divide. The 'planners' live in their skyscrapers, driving progress in the city without actually getting their hands dirty. The workers, however, slave away in a hellish underground. Freder, the son of one of the city's planners, discovers the horrible conditions of the workers and finds himself involved in all sorts of bizarre experiences.
And yes, this film is stunningly unusual. As I mentioned before, it's a bit slow, but the sheer scope of such an old film is breathtaking. I can only imagine how audiences responded to it when it was released. Lang's vision must have been unparalleled at the time. The imagery in here is incredible, covering all manner of religious and social observations. It's spooky, gradiose, and beautiful. While it might not necessarily be your 'cup of tea', every film fan should treat this one as required viewing.