The Bedford Incident. It came out in 1965, at the height of the Cold War (only three years after the Cuban missile crisis of 50 years ago this month) and it really reflected the era. It's about an American Naval officer determined to confront a Soviet submarine that has violated territorial waters. It does not end well. It's told in an almost documentary style, as I recall and though I haven't seen it since college, when it was part of the curriculum of a dorm course in political cinema, I still remember how shaken I was by the ending.
When I took Driver's Ed in high school, I was shown all those gory scare-fests that were so disturbing in some cases they were counter-productive. (I had a friend who was so put off by them that she didn't get her license until she was in her 20s. And a month after she got her license, she died in a car accident. I know, define irony.) I think that's why today I really hate the gory horror movies. I'm fine with "jump out at me" scary moments but I don't want to see blood and guts. Even if they are special effects.
The scariest movie I think I ever saw, though, was Jaws. I saw it the summer it came out and have seen it a couple of time since and since 1975, I have never, ever gone into the ocean past my knees. I know the chances of being eaten by a Great White Shark are pretty unlikely--although they regularly cruise between the beaches of Santa Monica and Catalina Island--but in the lizard part of my brain, I know that it's still possible. Jaws literally altered my behavior. I'd been an avid body-surfer up to the point where I'd seen the movie. (Or as much of a body-surfer as you can be at Virginia Beach where a really high wave is three feet tall.) I don't body-surf any more. I am very, very aware that in the ocean, humans are just visiting.
Jaws made me jump more than any horror movie I've ever seen.