First off let me say that Akira and Princess Mononoke are both must-see anime movies in the horror category (though neither of these is close to pure horror). Simply put, watch them if you haven't already.
Big seconds on Higurashi, Madoka, Steins;gate, School Days and Narutaru. Also, if you like Narutaru then you have to watch Bokurano which is by the same director. This one is pretty horrifying but on an almost entirely psychological level.
Of all of these Higurashi probably fits your criterion the best.
Another one that fits your criterion is the Kara no Kyoukai series. This one is almost ENTIRELY horror/suspense and is visually stunning. By that same token you might also enjoy Fate/Zero which is in large part actually a horror anime.
Some of my favorite oldschool Psychological Thrillers are Soultaker and Betterman. Soultaker is some of the craziest **** you'll ever watch, while Betterman is more of an under appreciated gem.
If you want something REALLY classic then check out Wicked City which was one of the most popular anime horror movies of the 80's. This one is over-the-top disturbing in almost every way.
You might also give Chrono Crusade and D. Gray-man a try but if you don't like action, the horror elements probably won't be enough to draw you in.
Also, Ergo Proxy is definitely suspense with a decent bit of horror. This show is like a big puzzle, in the same vein as Serial Experiments Lain, Boogiepop Phantom and Paranoia Agent
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