There's a big semi-sentient computer running the government in Idiocracy, which could make it a neat stand in for Skynet.

Idiocracy -> People become overly reliant on automation and complacent to the point of self-annihilation

Terminator -> Computers decide humans aren't worth the trouble, so they do a mass extermination

Matrix -> The conflict ends in a blotted out sky, which forces the computers to cannibalize humanity