Some excellent suggestions elsewhere which I have added in my to-watch wish list!
Mine (the line between horror and pyschological thriller can be thin);
28 Days Later
Alien
Asylum
Blair Witch Project (not trendy to like it these days, but in context of it being a micro-budget indie, it's good)
Carrie (surprised this had a mention yet!)
Don't Look Now
The Exorcist
Das Experiment
Invasion of the Body Snatchers (1978)
Misery
Nosferatu (I was lucky enough to see this with a live score, which was brilliant)
The Omen
Quatermass and the Pit
Shallow Grave (the first 18 I got into, under age!)
The Shining
Terminator
The Thing
Threads
Village of the Damned
The Wicker Man
Zodiac
Hammer House of Horror had three or four really good episodes. The Two Faces of Evil still stands up well now..
EDIT: Whistle and I'll Come to You has been recommended by the missus.