Let's try suggesting ones that people wouldn't normally think to suggest. After all most of us already know most and if we just say what everyone else is suggesting then we're not being too helpful.
I'll recommend Forbidden Siren on the PS2, it's a game that does a good job of making you feel cornered thanks to an interesting mechanic where you can see through your enemies eyes. In some cases you can watch them run right up to you and kill you before you can react. It does get pretty difficult later in the game as it focuses largely on using stealth to bypass enemies.
If you're looking for a more entry level Horror game i'd recommend Eternal Darkness, it's nice and linear and if you keep your character in tip top shape you should be able to breeze through the game without too much trouble. It doesn't pile on the subtle horror like Silent Hill and it doesn't have the jump scares that many independent horror games like to employ. A happy medium in between.
If you're not looking to break the bank then I recommend checking out a few indie horror games at various websites such as this one. A word of warning though, you really have to dig through these to find some that are truly great.
Have you played 7 days?
Game Link: http://gamejolt.com/games/7days/14592
Or IMSCARED?
Game Link: http://gamejolt.com/games/imscared-a-pixelated-nightmare/10058
Both are similar to what you are looking for. However, I feel that 7 Days may be more geared to the environment changing away from your view. IMSCARED also does this. I highly recommend playing both.
Perhaps it has now, this was a couple of days back. Also, there may be regional differences, I know for a fact Fatal Frame isn't even on the UK PSN, much to my chagrin. Update again; https://www.indiegala.com/halloween A pretty good bundle there, with the exception of fucking Real Horror Stories. Sang Froid and Paranormal are worth the $2.99 alone.
Forgotten Memories
https://play.google.com/store/apps/details?id=com.psychoseinteractive.forgottenmemories
I remember being excited for this game back when I first heard about the console ports, which have since been cancelled. I've never played it, but it seems to have good ratings. Support for modern gamepads has recently been added so I may finally get it. Thanks for reminding me.