Eternal Darkness: Sanity's Requiem
I was playing this back in the day, and my Gamecube came up with a disc error on the screen. My sanity meter was low so naturally, I waited for "THIS....CAN'T...BE..HAAAAAAPENNNNIIIIIINNNGGGG!!!"...but nothing...no button presses would get me back to the game screen. Five minutes later, I had to switch off the console and reload.
Had this had happened on any other game, I would have been a bit miffed and just got on with it, but this one always made me wonder to this day...was that an insanity effect, or did my game really crash...?
I suppose that's testament to the wonderful way this game got under your skin, no other game has had me questioning my own sanity like that!