Some interesting lists on here. Mine's in no particular order, as I can't really rank games (feels wrong to):
-Silent Hill 2: The first game gave me nightmares for a week. This game did that as well as made me afraid of the dark for the first time since I was a little kid. And you know what? I enjoyed it in the same sadomasochistic way that James himself probably enjoyed it.
-Mega Man Legends: This will hold a special place in my heart as being the first game I obsessed over. I'd explore every nook and cranny, and loved the near-seamless combination of the traditional Mega Man platforming with dungeon-crawling RPG elements. Legends 2 is probably the better game, especially since the controls were a lot smoother, but this one keeps the spot.
-Super Mario Galaxy: Sending a franchise into space might not be the most original idea out there, but damn if Miyamato didn't make the most of it. The use of gravity as a game mechanic is superb, if not a little mind-bending, turning what could have been yet another Mario game into one of the most unique platformers of this or any generation.
-Shadow of the Colossus: Ico also gets honorable mention here, but it's just not quite as awe-inspiring as it's successor. Lush environments, epic battles, and one downright amazing soundtrack wrapped around a plot that is deceptively simple, but with such dramatic weight to every single moment, whether it's that first shot of the Forbidden Lands to the fights with the colossi, to the mere act of wandering the landscape, looking for your next foe. An absolute find, and knowing that the next game from Fumito Ueda and company was going to be exclusive to the PS3 pretty much guaranteed Sony a sale for their system.
-Assassin's Creed: This one falls into the same category as Mega Man Legends, in that the sequel has better gameplay mechanics, but unlike that series, I'm going to say that the first AC is the better game. Not that AC2 was bad, mind you, just that it made a few wrong turns that undid everything: the narrative was a bit scattershot, it was way too easy to escape the guards compared to the first entry's glorious chase sequences, and most of the assassination missions felt very samey, with a few exceptions (about 2/3 of them consist of your buddies starting a fight to distract the guards while you sneak in and kill your target). The first game may have had some dull in-between segments, but when you got down to the assassinations, each one was a major setpiece. Couple that with the ambitious blend of Crusade-era politics, science fiction, conspiracy thriller, Islamic mysticism, and even a little Zen Buddhism (the controls seem to work best only when the player is calm and focused, compared to the usual instinct of manic button-mashing), and it's downright amazing.
-Final Fantasy VII: A.K.A. "When Final Fantasy Hit the Mainstream." It seems to be the fulcrum point for the series, since it did mark a distinct shift away from the medieval fantasy of the first six games and into more sci-fi territory (even the throwback ninth game had essentially an alien subplot), as well as the more anime inspired character designs, so some people hate it, and others love it. I'm in the latter group, obviously, precisely because of it's departure from the regular series. It borrows heavily from all those great sci-fi films from the '80's, like "Robocop" and "Blade Runner", and uses those tropes to explain how the Fantasy part of the game works. And, overexposure and absurdly overpowered fight sequences in later appearances aside, Cloud and Sephiroth make one hell of an antagonistic pair, with the latter goading the former into a one-way slide into madness for most of the game.
-Grand Theft Auto: San Andreas: Pretty much the reason why GTAIV left an underwhelming feeling for me was because it added a kinda/sorta cool addition (the cellphone that you can actually use), but stripped away all the advancements that littered San Andreas. GTA: SA is pretty much the best of the series so far, mostly because it offers a staggering amount of things to do: base jumping, weight-lifting, dating, buying businesses (yes, Vice City did it, too, but it still counts here), and of course the usual GTA hijinks. It also has the sharpest satirical edge of any of the games ("I Say/You Say"), evolving radio content rather than the constant loops of the other entries (my biggest gripe in IV, since it's the biggest step back), and a great cast voicing some fun characters.
-Okami: I love the Zelda series, but I think Okami beats it at it's own game. A Japanese sun goddess turning into a wolf and saving the world with painting is just the kind of uniquely videogame concept that I think only works in videogame format. And it's one of those games that's just astonishing to watch by itself, because rather than achieve the realism most other games set out for, it chooses a completely different style all its own.
-Shenmue: Never did get a Dreamcast, but a friend of mine did, and we had a ball playing Marvel vs. Capcom 2, Powerstone, Sonic Adventure, etc., but Shenmue was something else. It has that power of making the mundane seem more interesting (Ryo's obsession with collectibles being a point of humor for us. "Perhaps another?" indeed), and manages to seamlessly tie together it's disparate threads of adventure game, fighting game, and life-sim. I keep hoping for a port of the two Shenmue games to hit the PS2 or PS3, followed closely by a new game to complete the storyline, but like the Mega Man Legends series, I doubt there'll be any closure.
-Street Fighter II: Probably one of only five or six fighting games I even remotely like, SFII has a nice, colorful cast of characters with iconic attacks, and some amazing animation. If the action weren't so frenetic, it would just be a joy to sit there taking in what's on the screen.