No one has said Braid? I'm ashamed at all of you!!!

I will just make a list, as I can't pick just one.

Braid (due to the fact that it's the only game I've ever played that had a story that could absolutely not be told in a movie or book, only a game)

Half-Life series (The best Sci-Fi story outside of the book Ender's Game)

Modern Warfare series (Gripping, controversial, and above all the never-ending plot twists)

World in Conflict (Deals with themes like the value of Human life, sacrifice, forgiveness, and loyalty)

Company of Heroes series (Even though there's no central characters, it's about the trials and hardships of an entire company of men)

Mass Effect series (Deals with themes such as the place of humanity in the universe, and how to make an impossible decision)

Dragon Age: series (hard to explain)

Legend of Zelda series (not an individual game, the entire over-arching story that runs through-out the series. It's got some really great themes such as loss, betrayal, forgiveness, coming of age, willingness to accept change, heroism, and redemption.)

Final Fantasy VIII + X + Star Ocean 3 had some pretty amazing ones though. MGS games close behind.

FF6 for me because the character back storys where amazing and kefka was a total badass who completely destroys the world.

tales of the abyss and tales of symphonia. tales series always have godd good stories.

Here's some games stories that I've enjoyed over the years:

Sonic & Knuckles (Here's why I think so.)
Super Metroid
Metroid Prime
Bioshock
Conker's Bad Fur Day
Silent Hill: Shattered Memories

I suppose that I've chosen these games more on how they tell their stories rather than the actual stories themselves. But then again, I feel that how you tell your story is an extremely important part of being a video game, and sometimes more important than the story itself.

hotel dusk was great. Metal gear solid too

I don't think I've found a game out there that has even come close to any of the books, movies or TV series I have seen in solid plot and character development. Simply because games either focus too much on chunks of plot that lose their way (such as Final Fantasy and Metal Gear Solid games) or lose focus of the story as they have to focus on the gameplay, eventhough they still have good characters and powerful moments at times (such as Zelda games or Dragon Quest games).

Suffice to say, the games that I remember the most for their storyline are Suikoden I-III. Which can't be chosen individually, as all three games are an ongoing trilogy with interconnected characters and plot points. It did what I feel makes a story good in a game, which is focus on the characters and drive the plot by putting you in the role of interacting with each scene and event directly. You truly were the 'hero', as everything you did influenced the course of the games storyline, who joined your party, who lived and died and even how the games ended.

XENOGEARS

Betrayal at Krondor, easily.

"Parasite Eve", not only the best story in games but the best story period

The perfect mix between reality & science-fiction, i didn't read,played or watched anything

that comes close to the shear genius of that story

Hideaki Sena wrote a true master peace