I'd bet a lot of you haven't heard of LSD: Dream Emulator. For one thing, it was released only in Japan back in 1998. Furthermore, it was more of an experiment rather than an actual game, so there weren't many copies released. It's considered to be one of the rarest games on the PSOne, and it will be released in Japan's PSN Game Archives for the curiosity of those who've heard of it.
As its name implies, LSD: Dream Emulator will allow you to experience a "dream" through a game. These dreams involve many odd environments, odd elements, and different music, blended all into one very trippy affair. There's no objective, no action, and it's a little hard to make sense out of things until you get used to it. You'll get a better idea through this video.
LSD is so rare that its creator, Osamu Sato, saw the game fetch up to ¥18,000 ($210) on Yahoo Auctions. It's no Stadium Events, but that's still pretty rare too.
At any rate, the game will be hitting the PSN Game Archives for Japan, and it doesn't look like there will be a US or Euro release. Then again, if you're that curious, you should have no qualms about taking a trip down there and getting a copy.