The film is The Terminator, the 1984 film directed and co-written by James Cameron and starring Arnold Schwarzenegger.
The setting for the movie is 1984 Los Angeles. Schwarzenegger is an unstoppable cyborg built in the future, a future controlled by computers. In the year 2029, super computers and humans are locked in a battle to control earth. The cyborg has been sent back from the future to kill a young woman named Sarah Connor (Linda Hamilton). The computers believe that her death will alter the course of history and allow them to win the battle.
The humans of the future send their own champion back to 1984, too. He's a soldier named Kyle Reese (Michael Biehn--oh, baby). His mission is to locate and protect Sarah at all costs. Having grown up in the rubble of the post-apocalyptic future, he is overwhelmed by culture shock and by meeting Sarah.
Of course, they fall in love. That's the reason I like this movie so much. It's MY kind of romance--dark, quirky and erotic.
There are lots of clips of The Terminator online, but I've selected the trailer, which gives you a real sense of the thriller.