Traum is a short, story-driven game with horror elements. It encourages the player to explore as interacting with objects reveals more about the world, the story, and the main character himself. Many of the objects can be interacted with multiple times and some items trigger flashback memories of days past. During the gameplay there are also choices that will affect some future events.
Yume Nikki is a freeware game developed in RPG Maker 2003 for the PC, created by Kikiyama. It is unique in that it is one of the few psychological horror RPGs. The overall tone of the game is incredibly bleak, and very little of the experience is openly explained.
A survival horror doujin adventure game by Team GrisGris. It tells the story of a group of students trapped in a haunted elementary school. Originally released for the PC-98 in Japan back in 1996, it was not released in the Western world until 2011.
Absolutely horrifying game and a nod to Lovecraftian horror. Wish more similar games came out.