PI
This one is for the math geek. This movie is about a genius mathematician obsessed with finding patterns in numerical systems. He builds a computer that he names Euclid and tries to find patterns within the stock market. Soon he is being pursued by agents of a wall street firm who believe he has found the secret to predicting stock prices and a group of Hasidic Jews who believe he has found a number that is actually the true name of God.
SpaceballsWith lines like "Prepare for light speed..... No no no, light speed is too slow.... Light speed too slow? Yes, we're gonna have to go right to ludicrous speed", and "I see your Schwartz is as big as mine, but let's see how you handle it", this Mel Brooks Sci Fi parody is a geek classic. There's even a cameo from John Hurt with an alien ripping its way out of his stomach and Hurt saying "Oh no, not again".
Blade Runner
Science fiction movies based on Philip K. Dick stores and novels really deserve their own blog entry. This is the best of the bunch. It features Harrison Ford as a bounty hunter hired to find renegade android "replicants" who are for all intents and purposes indistinguishable from humans. Like all good Philip K. Dick stories, this one uses science and technology to ask deep questions. The big questions this time around: what does it mean to be human? and (shades of Turing), if a computer can't be distinguished from a human, then is it human?
Cube
I love movies like this. 'Cube' is about a gigantic cube consisting of rooms with various deathtraps. Seven strangers wake up in various rooms in the cube and team up to try to escape. Before the 'Saw' movies, were movies like this.
Army of Darkness"This... is my boomstick" I can't talk about geek movies without mentioning Bruce Campbell, and this is one of the most fun of his films. Bruce plays a man who is transported from modern times to the medieval age, and he must battle an army of the dead in order to find his way home.

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