I wasn't into the horror genre until like 15 years ago when I started studying and we talked about horror games. I said that I find the plots of horror games usually interesting but really dislike the gameplay which is way too hard for my taste. Someone recommended me to get Silent Hill 2 and play on beginner difficulty (for combat). I rented it and did as he told and absolutely loved the game. The fact that in beginner mode every monster dies from one or two hits with my trusty pipe and you don't die easily really made me able to appreciate the deep and philosophical story and being scared all the time is a great feeling too.
Ever since then I was always looking for more games like it. I played many of the Silent Hill games (enjoyed 3, The Room and Downpour too - admittably The Room was slightly too hard as it lacked difficulty setting and had invincible enemies, but I somehow managed) and also Fatal Frame 1-3 of which I enjoyed 2 the most as it had an easy setting (but it completely screws over the ending, I hate it when a higher difficulty is required for a better ending, bleh!). Had a hard time finding other horror games to enjoy. The Resident Evil series is absolutely horrible for me, like the opposite of what I like, it's way too hard, requires you to use guns and isn't even all that scary. And Alone in the Dark series is just way too hard. I absolutely loved Parasite Eve 1 and kind of still liked Parasite Eve 2. But in the end Fragile Dreams became my absolutely favorite horror game.
Later on I found out about the Trilby Adventure series which made me realize that Point&Click Adventure + Horror is actually the perfect thing for me. You can't die, you have all the time in the world, but at the same time you get a great mysterious horror story which can be really good and it can also be pretty spooky. There aren't many games in that genre, though. My favorite is probably "Missing", too bad hardly anybody knows about that one.
Always open for suggestions fulfilling the "hard/impossible to die in but are very scary and have a good story" requirement as I'm actually starved on that.
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As for movies / series, I have this weird thing that I don't like supernatural stuff which kind of filters out most. I loved the stuff that many others hate like for example the Saw series. I also love Cube and Cube Zero (but not so much Hypercube).
There are some absolutely amazing horror animes too. Especially Higurashi no Naku Koro ni.
Also always open for suggestions here, only requirement is that it's not supernatural (I'm fine with "scooby doo supernaturalism" as in it seems supernatural but at the end it's revealed that it was just an illusion).