Megaman 2:
This is still the gold standard by which I judge any 2D platforming action game.
Everything about that game is awesome, great bosses, great music and amazingly well designed levels.
Super Metroid and Catlevania: Symphony of the Night:
These are to side view exploration/action games what Megaman 2 is to side scrolling platformers. Both games are overflowing with atmosphere, they routinely reward exploration in a way that doesn't feel forced and both present you with a surprisingly large game world that keeps things fresh with new worlds, monsters and events that are all entertaining to play through (There's no part of either game that makes me roll my eyes and moan "Ugh...I hate this part.").
Silent Hill 2:
Not a perfect survival horror game by any standard but the story it tells is as close to as perfect a ghost story as anyone could hope for. Really the only problem I have with this title is that it did such a good job of creating Silent Hill as a character in and of itself that every subsequent title has felt somewhat bland by comparison.
Final Fantasy VI and Xenogears:
These are both nearly perfect JRPG's with characters and worlds that draw you in and keep you invested in the outcome of the story in very different ways.
Final Fantasy VI does an amazing job of presenting you with a story that, surprisingly enough doesn't seem to have a central character. Virtually every character in the game has a role to play as their personal story lines weave in and out of the metaplot. And unlike most games with a large cast of playable characters virtually every one of them is useful and fun to play (except Gao...the useless tit.)
Xenosaga on the other hand is all about the exploration of the world itself. The characters are all relatively blank slate archetypical characters but the world in which they inhabit is probably one of the most interesting and well crafted Sci-Fi/Fantasy stories I've ever played through.
While I admit it does tend to a lot of Navel Gazing and there's more than one section where the plot starts to drag, the overall presentation is so unique that these occasional dips in quality are easily overlooked.
I'm getting a little verbose here so I'll eschew the small essay for the rest of the list and just say that the rest of these games may not the the high point of their specific genre but they're still a damn lot of fun to play.
Devil May Cry
Dark Cloud 2
Burnout 3: Takedown
Metal Gear Solid
Metal Gear Solid 2: Sons of Liberty
Metal Gear Solid 3: Snake Eater
GUN
Hulk: Ultimate Destruction
La Pucelle Tactics
Mark of Kri
Rogue Galaxy
Red Dead Revolver
Okami
Legend of Zelda: A Link to the Past
Legend of Zelda: Windwaker
Diablo II
Warcraft III