The first thing that comes to mind is, bizarrely, the lead black-out windows going up automatically in Doctor Morbius (Walter Pidgeon)'s house on the "Forbidden Planet". Spooked me as a kid, watching it on TV. And the music ("tonalities") accompanying the coming of the invisible Id monster was pretty freaky as well.
In fact, I think my appreciation for movie soundtrack music probably came from seeing how effective music could be in the scariest parts of scary movies. The spooky music FX accompanying the astronauts finding the black monolith on the moon in "2001: A Space Odyssey" does it to me, too. I still cannot play the soundtrack when alone at night. If that track comes on I have to skip it forward to the next track.
"The Invisible Man", unwrapping himself in the British b/w TV series of the same name: he also gave me nightmares, but it was my Dad's favourite show at the time!
I never went to see "Alien" in the cinema, because I had a feeling that several scenes might be too scary, even as a guy in my early 20s at the time. Was very pleased I saw it on VHS first. (No problem watching "Aliens" or "Alien 3" on the big screen, though.)
Ah! And I just remembered! I was once followed home by a big black dog, at about 11.30 at night, after having seen "The Omen" at a local cinema!
Robbie the Robot vs Monsters Inc.