Ah, mentioning the gamecube made me remember of Eternal Darkness. Another "Not so hidden, but still rather obscure" game. The game presents strong lovecraftian horror, but with a twist: Sanity meters. That is, if a zombie (or other monster) sees you, your character loses sanity, which you can regain by performing a finishing blow on the monster. When your sanity starts dropping, you will start experiencing (un)sanity effects, which will get stronger as your meter lowers. Some of this effects go from mild things such as painting turning into hellish depictions, walls bleeding, hearing noises, to more extreme stuff as your character's head falling off randomly (which enables an option to recite the famous monologue in Hamlet), the game turning off the video or audio, bugs walking on the screen, and even the game deleting the save data. Pretty much, this game alone makes getting a Gamecube worth it. Here's a video of some sanity effects:
And here's a video of the autopsies of the monsters, with some great voice acting: