The original plot for The Matrix.
No, to drum up the fear, they've always had to invent a danger: "With a few keystrokes a team of hackers can blow up your house! Once computers get smart enough, they'll become sentient and start hating us! Robots will eventually cause the extinction of mankind!" And so on.
The whole idea is to play off people's ignorance on the subject. And people give them a lot to work with.
Will They Ever Stop?
It won't be long before the entire theater will be full of people who were raised with computers, and won't be all that scared of them. But that's OK--all that'll change is screenwriters will find new targets.
Soon you'll have less talk of a robot apocalypse, and more talk of a nanotechnology apocalypse, or a worldwide disaster caused by genetic engineering. As long as it's new and weird and unfamiliar, Hollywood scriptwriters will figure out a way to make it bring about the end of the world.