Most stuff by Acid Bath deserves a mention, mostly for the lyrics. It's not that they're gory, it's that they're downright unsettling in some cases. I'd recommend
The Scream of the Butterfly or Fingerpaintings of the Insane.
My Wall by Sunn 0))) is an excellent atmospheric piece with some interesting spoken word work in it. There's virtually no chance of me finding a link to listen to it as the piece is a half hour long, but it's worth listening to. I can't speak for the rest of their work, but that song is strangely mesmerizing.
Once again, disturbing lyrics: Comus. A strange folkish 70s band with songs about rape and murder. I'd recommend the song Drip Drip or The Bite.
Godspeed You! Black Emperor's Easting Hastings and The Dead Flag Blues both have some rather unsettling sections to them, and The Dead Flag Blues has an interesting poem in it with the subject of the apocalypse.
Whoever mentioned Pink Floyd's A Saucerful of Secrets was spot on. The beginning of that song puts me on edge. Same with the middle section of Echoes, but that song is mostly excellent, and not creepy save that annoying interlude.
Finally, the most disturbing song I can think of: World's End
Girlfriend's We Are The Massacre. I recommend not watching the video, and just relaxing with the music...until it begins. The screams fade in gradually from the background, while the music remains discordantly happy. Edit: Upon review, their entire discography has a creepy vibe to it.
And for the record, no, none of these are "screamers" or anything. I believe one of the Godspeed You! Black Emperor songs has a loud train whistle out of nowhere, but that's it. Enjoy, and have fun staying awake.