I'm talking single player experiences here, also. So please, no hatemail about Marvel Vs. Capcom 2, Smash Brawl, or Team Fortress 2 getting left out in the cold. They're great games, but this list is going for the quality of narrative and gameplay in single player experiences. For this reason, most puzzle, sports, driving, and rhythm games are not in contention. (Sorry Pac Man, no cerebral resonance.)
Here 'dem is (in order of the character length of their familiar titles):
Final Fantasy VII
Shadow of the Colossus
Controversial, I know. "No Zelda?" I'm afraid not. I'm a big fan of Ocarina and Majora's Mask, but those games don't have any real emotional value tied to their story. Zelda games are what they are, but I've never spent any time thinking about them after the fact like I have the list members.
Portal, if you have played it, is self-evident. An anti-shooter, if you will, it defies all convention. This first-person puzzler is so unique, and presents such a compelling plot even with the near total absence of other characters.
BioShock may seem like jumping the gun, as I obviously completed it pretty recently. But this really did edge out Half-Life 2 or Half-Life 2: Episode 2 as the best FPS I've ever played. Just check any of the BlogoShock posts to see why.
MGS 1 and 4 are also both great games, but Metal Gear Solid 3: Snake Eater holds a very special place in my gamer heart. Definitely the most emotionally invested I've ever been in a game. Great characters, immersive atmosphere, and top-notch stealth action. (Man, I could go for another playthrough right now...) Solid Snake is a complex, beloved character, but he is no Big Boss.
Final Fantasy VII is a tough one to pick, as the gameplay has aged significantly. This one is a total classic, and the storyline, that is to say, the complete storyline, made this the definition of the word "epic" in the gaming lexicon. Breadth, depth, and scope all revolutionary for it's time. It is the kind of game, like Snake Eater, that is always worth a challenge playthrough, not just for the bragging rights, but to enjoy the experience all over again.
(I actually debated a lot between inclusion of Final Fantasy VII or X-2. X-2's gameplay I believe is the best in the series, and I am looking forward to a return to the formula for XIII, but VII's plot and characters outweigh X-2's frenetic battle system.)
Shadow of the Colossus... well, if you haven't played it, you need to. And once you play it, you know.