Colossus: The Forbin Project (1970)

Before Skynet, there was Colossus. With typical military wisdom, the US Government turns control of its nuclear arsenal over to an artificial intelligence named Colossus (or course the lead scientist says it is incapable of actual thought), which is built inside the heart of a mountain which makes it impervious to human intervention. What could possibly go wrong? Especially when the AI learns it isn't the only new kid on the block.