I'm overall not a horror fan, but there are two horror games I've actually played. First of all Phantasmagoria. This game may not be really famous anymore, however it was designed by Robertta Williams who also brought us the King's Quest series, and the game was developed by Sierra On-Line. The game was notorious for the need of SEVEN(!) CD-ROMs in order to play it. In the game you assume the role of a young woman who just moved with her husband to a mansion. While her husband is trying to get several things done to make the house suitable for living, you explore the house and eventually discover it was once owned by an evil guy whose spirit still lingers in the place and eventually takes possession of tadaa... your husband, who as a result goes mad and becomes more and more dangerous. You will also get some horror illusions among the game. The game does not work in jumpscares, but rather in a mood that gets creepier the more of the game you have solved.
The other horror game is Alice: Madness Returns, and I need to note that this is a psychological horror. You assume the role of Alice Liddell, the heroine of the Alice and Wonderland story. Traumatized by the fire that destroyed her house, and killed her parents and sister she is getting therapy by Dr. Bumby in order to forget all about that fire. This makes sense given the fact that Alice in Wonderland takes place during the Victorian era of the U.K. and back in this years it was a general consensus that whenever something bad happens you have to forget about it and move on (having traumas myself I know that this ain't gonna work, but today that is acknowledged, but this idea is pretty new). Alice however gets madder and madder, and seeks refuge in Wonderland, the world of her own imagination. However as the game progresses, Alice will actually get crazier and crazier until the moment the culprit of the murder and fire pops back in her memory (whose identity I will not reveal to prevent spoilers). The crazier she becomes the more horrible Wonderland looks, since it's nothing more but a reflection of her own mind. Once again, no jumpscares, and maybe not even that you sit on the tip of your chair out of fear, but yet a creepy mood that gets creepier all the way as Alice nearly "drowns" in her own madness. Especially when you see her memories of being in the madhouse (which is enough to get anyone crazy, and some of the "treatments" (read well-intended maiming) are actually historically correct, to make matters worse) you know you can better not play this game when little kids are around (the game does in the EU have an 18+ rating).