I'm honestly in the same boat as you, sci fi and action were my go to genre growing up but mu sister was a horror fan so i saw mu fair share of duff b horror movies. Ironically exactly the sort of thing that Cabin in the woods parodies. I enjoy a couple of them just purely because i can switch off a little when they're on but i'll be honest the only horror films that've truly creeped me out after watching them are oriental horror. I can't believed that no one on here recommended Ju-on the grudge and Ring. Both are creepy as dicks if watched alone in the dark, ignore the us remakes they're poopoo. Dark water and the eye (again the remake is crap) have some tense moments as well, no killable monster, no rubber masks, no serial killers just a great attention to tension growth effects and slowly escalating dread.
There are a lot of games out there that'd fit into the horror genre and they're getting better, i personally find that as soon as you have a gun in your hand then a game looses its tension. I seem to remember AH playing a game called PT recently that looked pretty creepy though.