Some well-written stuff that is also scary (I'll leave out the non-fiction, too much material there):

T.E.D. Klein writes very little but what he writes can really put the chill in you.  All suggestion, no gore. Primarily known for adding modern urban worries to Lovecraftian cosmic horror.  He's best known for "The Ceremonies", a novel, and a collection of 4 novellas, "Dark Gods"  I'd start with the novella collection, all are amazing.

Richard Matheson and Charles Beaumont were a couple of the bright lights of the modern horror movement of the 1950s and 1960s - pick any collection of their short stories.

Algernon Blackwood wrote a short story called "The Willows" (Google it - it's out of copyright and you can find the whole story on several sites) about two men canoeing down the Danube who get stuck on an island and find... something.  Very disturbing story, do NOT read this before you go camping.

Shirley Jackson's "The Haunting of Hill House".  This is one of the few examples I can think of where the book and the film adaptation (the original black and white, not the remake) are both equally excellent.

And for good measure, check out Matheson's "Hell House".

Some of Jorge Luis Borges' short stories are existentially scary, as literature and the real world merge together.

F. Paul Wilson is keeping his Repairman Jack stories very tight...great combination of action/mystery, about an urban "fixer" who lives off the grid running into a war between genuinely scary cosmic forces (he's written other stories which fit into the same "Adversary Cycle" - see if you want to jump in.

Really disturbing: "The Sound of His Horn" by Saban.  Look for this in the library or used book store, may be hard to find nowadays.  An Englishman slips into a parallel future where the Nazis won WWII and hunt genetically-altered humans for sport.

Ray Bradbury's early horror stories, mostly collected in "The October Country" have a cold, scary edge that was lacking in some of Uncle Ray's later stuff.  Some genuinely scary classics, like "The Jar".

Not normally thought of as horror, but Carson McCuller's "To Kill a Mockingbird" I always found kind of spooky (the book and the movie), as kids try to deal with outside forces beyond their understanding (the scary "different" neighbor, racism, etc.).  It really captures that time when your neighborhood was the whole universe.

Ambrose Bierce wrote what is probably the most ripped-off short story in history, "An Occurence at Owl Creek Bridge".  Look for some of his short story collections and look for "The Damned Thing".

Invalid, if you're into Russian Lit check out Isaac Babel if you haven't already.  His "Red Cavalry" (a series of short stories based on Babel's experiences as a Red Army propagandist in a Cossack cavalry unit during the failed 1920 invasion of Poland finds real horror in the casual cruelties of warfare and the way it changes the protagonist.

Kent Anderson's "Sympathy for the Devil" is a Vietnam novel that reads a little like a horror novel (Anderson was Special Forces).  The sequel "Night Dogs" is a cop novel that is uneven but worth reading and is also a little scary.