Games like Amnesia and Outlast will feature highly in any recommendations, but I find them to be boring walking funnels. Instead I'd recommend something like Dead Space which is much more fun an experience.
SOMA... maybe it's more creepy than truly scary (still it is described as a sci-fi horror game), but the story was just so good. And it's from the same studio that gave us Amnesia: The Dark Descent. (and Rebirth, which is apparently not that great)
I'm a total wimp in horror games so Alien: Isolation was a terrifying experience for me.