Dear Esther is a horror game now?
Clive Barker's Undying is without a doubt my favourite horror video game. It was my reigning scariest-game-ever until Amnesia came along. It's really old though, mind.
If you like adventure games, Ben Croshaw (of Zero Punctuation game), made a bunch of well-written, low-fi horror games called the Chzo Mythos. The games are in order: 5 Days a Stranger, 7 Days a Skeptic, Trilby's Notes and 6 Days a Sacrifice.
There's the Silent Hill games that have represented horror games for years, but I haven't played any, except for a bit of the first which I thought was genuinely scary.
If you liked Amnesia, consider Frictional's previous efforts, namely the Penumbra series. They're the games most similar to Amnesia.
Then there's an indie game that's been grabbing the survival horror headlines, called Lone Survivor, by Jason Byrne. Not sure if it's classic horror or not, so look into it.
As for games coming up, there's Anna by Dreampainters, which looks like an interesting horror adventure thing (and close to Amnesia/Dear Esther). It's coming out next month.
Finally, there's the sequel to Amnesia, being developed by the Dear Esther team, called A Machine for Pigs.