With so many great games, I decided that the way to make my list would be to list the games that still are the best of their kind, at least in some aspect. The games that I can point to today and without hesitation say to play them before any other games in their series or maybe even genre.
Also: In this ballot there be spoilers
Without further ado, the definitive, disagree-and-you're-wrong best of the generation:
1. Resident Evil 4 ; In it's genre, it's still better than anything before it or after. It has better pacing, better game mechanics, better variety, better just about everything. When this was playable at E3, I played it every day. On the last day, they literally had to pull the plug from the machines before I stopped. Today, it still stands as a monument, a challenge that has yet to be overcome. Games like The Last of Us may have surpassed it in presentation, but when it comes to play, they're honestly not even in the discussion. Then it went and included Mercenaries mode, a side game that was still better than the vast majority of games released that generation or even last generation.
2. Silent Hill 2 ; BioShock. Portal. Dead Space. Gone Home. The topic of environmental storytelling has been a hot topic since at least the days of Myst. But to this day it still hasn't been done as well as Silent Hill 2. More effectively than any other game, even in its own series, Silent Hill 2 captured the psyche of the main character and told us a story through his environment. Every room told a story about James, about his guilt, his conscience, and his relationship with his wife. Nowadays, to get the point across, games will typically stick you with a sidekick NPC that might as well be named Morgan Freeman with how baldly "the point" and the significance of everything is said to you. That, or they litter audiotapes of characters recording messages to the player in a way that is completely incoherent with the game world. Silent Hill 2 was all about everything fitting in place and ultimately respecting the player. Something that games all too often fail to do these days.
3. Metroid Prime ; Speaking of environmental storytelling, here's another game that exhibits incredible mastery of it. The main difference between this game and Silent Hill 2 is the sense of empowerment you get as you familiarize yourself with the world. The intruder becomes the hunter. With some of the best music ever composed for a videogame, incredible visuals designed to immerse you (the visor effects are still cool as hell), and elegant solutions to platforming in first-person, and shooting in what is really an exploration/puzzle game, Metroid Prime set the bar for first person exploration and still hasn't been matched. AniHawk, my apologies.
4. Sid Meier's Civilization IV ; The best Civ game.
formerly: Sid Meier's Alpha Centauri ; The recent release of Beyond Earth really made me appreciate even more how special Alpha Centauri was. The worldbuilding in this game is stunning -- one of the best works of science fiction, including novels, films, and so on. The tweaks to the standard "Civ" formula worked out to be even better than Civ itself and encouraged a diverse set of playstyles. Now if you'll excuse me, I have to get back. The drones need me. They look up to me.
5. F-Zero GX ; Simply put, there isn't a better futuristic racer on this earth. For my money, it's actually the best racer ever, bar none. In a way, it actually reminds me of Punchout in the later rounds. This is a game that demands perfection at every moment, that pushes you to get better. And when you climb that summit, when you attain it, it's all due to your own will and skill. This game gives you nothing; you must take it. And when you finally do, you truly feel like a god.
6. Shadow of the Colossus ; One of the few truly majestic games out there. It takes a simple concept -- take down giant bosses -- and makes the whole game about it, and it's better for it. By shedding all the other meaningless crap, time is created; Time for the creators to focus on making those monstrous battles as impactful as possible, and time for you between battles to wander, to explore, to reflect. This is a game that revels in wilderness, that feels so melancholic and empty that it seeps into your soul. The central mechanic of this game -- holding on, against impossible odds -- is a perfect metaphor for what the character is going through emotionally, and what sets this game apart from the rest. The finale strikes hard with that metaphor, in a moment of pure beauty.
7. Beyond Good and Evil ; A little uneven (the insta-fail sections are still kind of bogus to me) but the characters and world is sublime.
formerly: The Legend of Zelda: Twilight Princess; A slow opening is made completely worth it by the best side character in the Zelda series, and the best collection of dungeons in the series on top of it. It doesn't reach the heights of the Zelda greats -- the ending isn't as good as Ocarina's, the mood isn't as good as Majora's, and so on -- but at least in dungeons, this game is on top. Combine it with a fantastic soundtrack and a nod to westerns that made me grin ear-to-ear, and this deserves a spot on the list.
8. F.E.A.R. ; For some reason, shooters today still haven't figured out how to make combat feel as good as this game. Shooting guys never felt so fucking awesome as it does in this game. Hearing troops flank you, hearing the chunky sound of bullets and explosions in slow-motion, and the clean, functional arenas make playing this game a joy. Everything is so weighty that it feels practically tangible. And there's still no better feeling than pinning dudes to the wall with your nail gun. I don't know why more games can't get the feedback right, but damn does this game feel amazing.
9. Grandia II ; This game made a constant companion to my Dreamcast for the entire time I had it. With its likable cast of characters, its big, clean graphics, and the best battle system ever put in a RPG, this game charmed the hell out of me. Yes, the story is generic, but the rest was so good that I didn't care.
10. Katamari Damacy ; One of the most joyful experiences of the generation, and there was really nothing else like it. The mechanics are simple and inviting, and they're something anybody can understand and get into. Everything from the visuals to the music is infectious, you want to roll it all up into your life. The later games lost the magic charm for me, but this game will always hold a place in my heart.
x. Civilization IV ; It's a fantastic game, and realistically it's number eleven on my list, but I had to bump it because I'd still rather play Alpha Centauri.
x. Animal Crossing ; I have such damn fond memories of this game, playing with dormmates. It pretty much invented its own genre, which can't be dismissed. But it was also surpassed with later entries. I can't say to play it today, which bumped it down to honorable mention.
x. Battlefield 2 ; The last time Battlefield was truly incredible to me. Every game is trying to recapture the lost magic of this game.
x. Super Smash Bros. Melee ; I really wanted to keep this up there, but it's been surpassed by Smash 4. And it didn't invent the genre like Smash 64 did.
x. Killer7 ; Incredible but ultimately too flawed for the Top 10. Still, it's Suda51's second-best game, right behind No More Heroes. This game should be ported to Wii or Wii U already with updated controls. Come on.
x. Halo 2 ; There was a lot of online bullshit with this game, but that almost added to the thrill. I loved the ranking system, I loved the map designs. This was Halo when it still felt somewhat raw, when things could be abused in a way that was still fun, and was still a complete thrill ride. Landing a sticky on a guy's face is still as fun as it is a double entendre.
x. Mother 3 ; One of the most beautiful stories ever told in a game. Proof that you don't need the fanciest graphics to leave a huge impression or tell a good story.
x. Shenmue ; It's hard to think of worlds I'd rather get back to than this one. This was an eye-opening, immersive experience. It somehow made the mundane feel magical.