Tetris - The "Citizen Kane of games" that everyone has been waiting for came out before we were taking games seriously. The recorded narrative that makes you feel is literally you getting apprehension, anger, grief, elation, and pure flow state oneness while you yourself play the game, and sort blocks into lines. This game is a slap in the face of anyone that thinks we need the trappings of film to be art.

Portal - Just such a novel game and mechanic, a clever and fun tone, everything fit together properly. Some days I'd change this out for Quake as the mirror of this.

Shadow of the Colossus - What a fucking game.

Dwarf Fortress -My "everything" game. I just want it to keep growing.

And I don't know about the fifth. I'll have to get back to you. Maybe Quake, maybe a GTA, maybe Minecraft. I just don't know.

/edit: Final Fantasy 6 - I'm not saying narrative is bad in my earlier explanation. I'm just saying it's not inherently the medium's strength. But this is great. And the community's mods ("romhacks") are just chef's kiss.