The Terminator (1984)

Before the sequels and the franchise, this was a tense, low-budget chase movie, and it's all the better for it. The science is where it falls down. The time travel makes no sense, and there's a paradox right at its heart: Kyle Reese goes back in time and becomes John Connor's father - but John Connor is the one who sent him back. So who came first? There's no good answer to that. To be fair, The Terminator is far from alone here - paradoxes like this are a problem in almost every time travel film. But look at the prescience. An AI defence system deciding that humans are the threat seemed far-fetched in 1984. Now "Skynet" is shorthand for a genuine worry that people take seriously. Not bad for a film made on a shoestring.