To me horror is all about atmosphere and mystery - not knowing what's around the next corner. While I love Resident Evil to death, they've never been horror games to me. Resident Evil 1 had a great atmosphere - creepy abandoned mansion in the mountains, doors are locked by an odd knight-based key system, strange puzzles everywhere that lead to 'what do I even do with this item I got from solving it' situations, etc. - but if you're playing as Jill, within fifteen minutes of the start you can have a handgun, a shotgun, and a grenade launcher to take everything down with + a competent partner (Barry pretty much owns Plant 42 for you if you're too lazy to make V-Jolt, although as a sidenote I always found it hilarious he just happens to have a flamethrower on him when he walks in the room. I guess Wesker gave it to him?), and with a little careful planning you can finish the game -easily - with way too much ammo and herbs. On the other hand, I dislike every Silent Hill save for the first two, but those games have excellent atmosphere. The fog covering everything, the odd NPCs, the fact most weapons are improvised melee (and you WANT to save what ammo you get), and having a radio crackle with different types of static based on what kind of enemy is near with the volume indicating how close they are... that's brilliant. The puzzles were great, too. For example, the 'face' puzzle in Silent Hill 2, where you had to figure out what buttons to press on a door in what order based on a somewhat disturbing poem.
To be fair, Horror is different for everyone. Some people probably actually get scared watching, say, the Friday the 13th series. I think the series is awesome, but that's just me. I guess the best example of 'horror' I can give you is Alan Wake. It presents the idea that there are forces out there beyond the reckoning of man and while we can, to a small extent, fight and maybe even control them (Wake's power to make things happen by writing them), we'll never be able to truly understand or defeat them. As a game it has excellent mechanics; as a story every element works. To a lesser extent, Eternal Darkness is similar, but it's too... Cthulu without actually being Cthulu. Sort of like what Trevor Moorehouse is to Jason Voorhees... the cheaper, Wal-Mart brand, y'know?
Anyway, just my thoughts on the matter.