Majora's Mask. The way you interact with all the characters, their stories, how you help them... It really makes you feel connected to them. For me, no other game has done that.
Right up there too: Link's Awakening, Wind Waker, Skyward Sword, Chrono Trigger, Final Fantasy VI and IX, Crisis Core, FRAGILE DREAMS, Limbo, Half-Life 2 and it's episodes, Bastion, Metro 2033, among others I don't remember right now.
FUCK! You've reminded me of this game! This gem of a game! I was never unable to beat it due to a crazy bug, no matter what I did, right after getting kissed by Crow, then running around a bit the game freezed and could never progress beyond that point. It was a very beautiful, well-crafted game, despite its rough edges with the controls, which were floppy. How was the game? Was the ending good? The story was very, very interesting.