http://en.wikipedia.org/wiki/LSD_(video_game)I feel like, in some respects, this might be the granddaddy of notgames. It plays like any number of early 3d games for the PSX or otherwise, but all you do is effectively walk around and explore and examine the changing scenery. Touching walls/objects will usually warp you somewhere else, and if you jump into a chasm you'll wake up. And sometimes your nightly dream is replaced with a completely unrelated video clip. And there's certain events that can happen which affect the dreams.
... it's hard to adequately describe the experience.
I'd love to see a modern remake of this, given all that can be done nowadays with modern graphics cards and procedural generation and the like. But at the same time, I think the primitive PSX graphics really drive home the fragile and dream/hallucination-like feel.