The original Resident Evil. It was unlike anything I'd experienced before. The sense of mystery and discovery as I worked through the game and the story gradually unfolded was incredible. I can't recall anything matching that feeling.
Shout out to Super Mario 64 (first time controlling a character in 3D with a joystick was mind blowing for me) and Super Mario Galaxy (got it for Christmas after release and was up til about 4am playing it. Someone used the word magical to describe it here and that is spot on).