I am gonna go a bit old school on you guys....
Another world, which came out in 1991 for the SNES was a scary game for me. You started the game off with no story, just you in a cage. You break free and this giant unstoppable gorilla chases you, and if he catches you, you die. You flee for your life and you don't know where you are, and everyone is against you. You are completely alone in an alien world. You can't communicate with anyone and you have to survive on pure instinct. I gave a very surreal survival feeling, one that creeped you out completely.
I've always enjoyed horror movies, so zombie games and the like don't scare me. The original Doom was scary enough, and I was like, 10 or so when it first came out (maybe I was 12 not sure) and I thought the noises the daemons made was eerie. Ever since then everything has been a rehash, so not too scary.
Alone in the Dark, is another series of games that started out in the same manner, no story introduction at all, you just started the game. As you progressed you unlocked bits and pieces of a crazy dark story line.
They don't make games like those anymore.