No particular order, and there are games I left off. There are just too many great games to make anything other than a top 20-30.
Earthbound (Honorable Mention for Mother 3)
It's an old-school RPG that understood that game elements are can be secondary to game experience, and the Mother series is good about being an experience first and a game second. While the gameplay elements aren't exactly innovative or stellar, it's still a great experience and the sort of game that took weird all the way to the bank, and did it well. It is the Hitchhiker's of gaming.
Breath of Fire IV (Honorable Mention for Fallout 3)
Atmosphere is a part of a game that can by itself make or break a narrative. Breath of Fire IV went the entire nine yards with atmosphere, while still having all of the elements of good gameplay attached that made the game both a functional game, and a functional narrative. The music was all very stylish, the characters tangible, and the world very real. If only Fallout 3 had been just a little more spot-on, it would've had the spot. These games are good because of good games, but great because of atmosphere.
Legend of Mana (Honorable Mention to Saints Row 2)
Legend of Mana had potential to be the best game possible for its genre. Legend of Mana is a bizarre sort of "build your own world" game that gave you the ability to assemble the world to your whimsy. This, coupled with a wide variety of play styles and in-game capability for customization, made it a contender in the Top 5. Saints Row 2 is really close because of the Sandbox-nature of the game and lets you really play with your avatar, personality, and character.
Shenmue (Honorable Mention to Star Wars: Knights of the Old Republic)
In a game designed to give you a large area to play, with fun gameplay and a compelling story, the pick between Shenmue and KotOR felt too close to call. But in the end, Shenmue won out for going the little extra mile for main content. Although I will give KotOR credit for actually completing its story. I will give Shenmue credit for actually manufacturing an enjoyable QTE system, especially for being the first ever. Something that nearly every progressive game that has tried and failed at.
Mirror's Edge (Honorable Mention to the Halo series)
It takes a lot of balls to do something completely unheard-of and weird with a genre, and Mirror's Edge is a first-person "shooter" that prides itself on doing something completely different with it. It's a game that knows what it is, tries something it's capable of, and pulls it off with flair. The Halo series gets a mention for being the first FPS that really jumped from the PC ocean to Console and made it big despite pre-conceived notion of unfit controls.