Most of the great ones have been recommended!
I'd like to throw in a few more that may qualify
Shikabane Hime Aka - a.k.a. Corpse Princess. These girls are living corpses, contracted to monks. Though the series heavily relies on action, it does have it's fair share of horror scenes.
xxxHoLiC - This should be classified more under psychological/supernatural as the protagonist can see spirits and works with a witch to fulfill wishes, though..not without paying a price. Some episodes were chilling because you never know what price the person has to pay.
Mouryou no Hako - Investigating the murders of schoolgirls who have been stuffed into boxes. Very dialogue-driven but leaves you thinking.