What is your fear... made of?
The Fatal Frame series (or Project Zero)...
For those with a "tendency" to fear spirits, ghosts etc...
Or do you like bloody horror?
(Game: "Siren")
Do you like having a chance to fight?
edit: Penumbra is more like 'puzzles' than 'battles'. Just fyi
(Game: "Penumbra: Overture", same producer from "Amnesia")
There is one more I'd like to list... A game when you flee from an enemy, a Picture-in-Picture shows the "monster" view, chasing you. Pretty scary.
But the Penumbra was a game I couldn't really finish. The physics are so... intense
Fatal Frame has some scary moments... One was on FF2, when I opened a closet, there was a small, female doll (there are dolls all through the game, some on gibbets etc), and when I changed to "camera mode" to look at it, when I was concentrated, and focused at the doll, it moved his head and looked at me.
I threw the control away and went to take a bath. I was dripping sweat @ 4AM.