Before Skynet, there was Colossus.
Colossus: the Forbin Project is a 1970 sci-fi film about an American supercomputer that joins forces with its Soviet counterpart to take over the world. Most people haven't heard of this movie, but it is a superior piece of film-making with a tight, intelligent script and fine acting. It set the model for "supercomputers and nuclear weapons don't mix" movies, and while later films like the Terminator franchise are flashier and far more violent, Colossus is a more compelling film with some psychological depth that bears re-watching in a way that the newer movies often don't, for me anyway.
One thing I like about it: the bad-guy computer in this film isn't so much evil as it is simply, coldly, logical. HAL 9000 malfunctioned due to a programming conflict, while Skynet often acts like a James Bond cartoon villain. Colossus is smarter and doesn't toy with people or kill them unnecessarily. It's a great flick.
The clip posted above actually gives away the ending, so don't watch it if you aren't familiar with how the film ends.