Colossus: The Forbin Project (1970)

This science fiction movie (adapted from a novel) is a template for lots of other "computer becomes sentient and takes over the world" tropes. But the computer's not malfunctioning; as it explains late in the film, it can just do a better job at protecting humanity than they can.

Dr Forbin creates Colossus as a coordinated nuclear defense system for the U.S. No sooner is it activated than its detects its opposite number in the USSR, links up with it, develops a mathematical language from scratch, and threatens to destroy cities if its demands are not met.

We don't get a lot of special effects, but we do get 1970's style, a tense atmosphere, and a before-its-time commentary on the surveillance society. Dr. Forbin is forced to live every moment under his computer's eye, so he can be monitored for threats. Forbin teaches Colossus how to make the perfect martini! Colossus' self-designed voicebox replaces his clunky teletype output with a smooth modern and yet menacing look.

The whole thing is just a little cheesy and takes itself pretty seriously. But if you want to root for the computer to win, Colossus is the villain for you.