And the moral of this story is ... never have two phone lines in the house.
I'm sure that the "twist" of this movie is a surprise to almost no one - even people who haven't seen the film know the story as a kind of babysiting urban legend - but I'll try not to spoil it. A teenage girl (Carol Kane) is babysitting two kids. She is downstairs watching television or something while the kids are upstairs asleep. She gets several anonymous phone calls, first just heavy breathing, then the question "Have you checked the children?" The calls get increasingly creepy and the babysitter eventually calls the police, who say they'll trace the call. And ... that's all I'd better say about that.
This movie was originally supposed to be a sequel to Black Christmas, which I've written about here and which has a similar setup with characters getting threatening phone calls. Apparently, they hoped to make a sequel to BC out of what eventually became Halloween as well, but both Halloween and When a Stranger Calls became stand-alone films. There was a sequel to When a Stranger Calls in 1993, also featuring Carol Kane, and it's one of the rare sequels that's every bit as scary (perhaps more so) than the original.
This is a VERY suspenseful and quite scary movie, without being bloody. It reminds me a good bit of Wait Until Dark, actually - if you've seen that, it's that particular kind of scary. When a Stranger Calls kind of dies in the middle, but the opening and the finale are absolutely heart-stopping.