The Mass Effect Mega-Narrative (i.e. the Story that encompasses both games and the companion novels), it's a story that engages the player on a personal level by giving them unparalleled control over events in the game. It's fantastically cinematic and you get to see consequences for your previous actions, even if they're minor. As well the Universe that surrounds Mass Effect is incredibly deep and interesting, even if it is a little unoriginal.
Suikoden 2, in spite of its poor translation and as a testament to the true power of its narrative, this game is a brilliant depiction of war, ideology and it's tole on friendship and contains two of the best villains ever seen in the videogame world. The monstrous Lucca Blight, and the other far more subtler villain who acts as the real antagonist of the piece. Those who have played know who I'm talking about, a "villain" who does all the wrong things for all the right reasons and is only trying to bring peace to a war ravaged country the best way he knows how.
Persona 4 an awesome mystery filled with tons of likable, funny and realistic characters with a supernatural element and so many dark, emotional moments and surprising twists you might think your soul will break. It also allows a great deal of player control over the story and provides an amusing "simulation" of the life of a Japanese Highschool Student in a small, sleepy town in the countryside.
Extremely Honorable Mentions
Silent Hill 2
Silent Hill 3
Bioshock
Half-Life 2
Portal
Suikoden 5
Xenosaga 3
Final Fantasy XII
Final Fantasy VI
Dragon Age: Origins
Knights of the Old Republic
Metal Gear Solid 3: Snake Eater
Baldurs Gate 2
NOTE: Don't beat me over the head for not including Planescape: Torment, I've only played a bit of it and I've never been able to find a copy.