One of the most notable ones I can think of is LSD (Lovely Sweet Dream): Dream Emulator

In this game, when you touch anything, you're teleported to another area in a dream world. Most events in the game are scripted, but they will happen in new and random ways, and after a while, you may notice patterns.
In my experience, and in that of some other players of the game, the game builds patterns based on the individual playing.
For example, a person I know would play the game a lot and conditioned him to react to the "Grey Man" (the seemed antagonist of the game) and it would cause the Grey Man to appear in precise ways that would frighten this person.
I should also mention that the guy playing the game is not easily scared. I'm not just saying that; he really is unaffected by most "scary" games.
Anyway, does anyone know of similar games that seem to be "sentient" or "possessed"? If so or if not, do you have any experiences with this kind of thing in general?
TL;DR: games where spooky stuff happens that doesn't seem like it's supposed to happen but seems to happen specifically to you