Hey, the PSOne was released in 2000, and so was Vagrant Story. Does it count? C'mon!
updated the first post.
anyway, here's a list of games that have currently received votes and/or honorable mentions:
Ace Combat 4
Ace Combat 5: The Unsung War
Ace Combat Zero: The Belkan War
Advance Wars
Advance Wars 2: Black Hole Rising
Age of Empires II: The Age of Kings
Age of Empires II: The Conquerors
Age of Mythology
Alien vs. Predator 2
Amplitude
Anachronox
Animal Crossing
Ape Escape 2
Ar Tonelico: Melody of Elernia
Ar Tonelico 2: Melody of Metafalica
Arcanum
Arx Fatalis
Atelier Iris
Baldur's Gate II: Shadows of Amn
Baldur's Gate: Dark Alliance 2
Bangai-O
Batallion Wars
Baten Kaitos
Baten Kaitos Origins
Battle Realms
Battlefield 1942
Battlefield 2
Bejeweled 2
Beyond Good & Evil
Black
Bllinx the Time Sweeper
Boktai: The Sun Is in Your Hand
Bookworm Adventures Deluxe
Breath of Fire: Dragon Quarter
Bully
Burnout 2: Point of Impact
Burnout 3: Takedown
Burnout Revenge
Call of Duty
Call of Duty 2
Call of Duty 2: Big Red One
Capcom vs. SNK 2
Castlevania: Aria of Sorrow
Castlevania: Circle of the Moon
Cave Story
Champions of Norrath
Championship Manager: Season 01/02
Chibi-Robo!
Chu Chu Rocket
City of Heroes
Civilization III
Civilization IV
Command & Conquer: Generals
Command & Conquer: Generals Zero Hour
Command & Conquer: Red Alert 2
Commandos 2: Men of Courage
Contra: Shattered Soldier
Cosmic Smash
Counter-Strike
Counter-Strike: Source
Crash Tag Team Racing
Crazy Taxi
Custom Robo
Dance Dance Revolution Extreme
Dark Age of Camelot
Dark Cloud 2
Day of Defeat: Source
DDRMAX2: Dance Dance Revolution 7th Mix
Dead or Alive 2
Dead or Alive 3
Dead to Rights
Def Jam: Fight for NY
Destroy All Humans
Destroy All Humans 2
Deus Ex
Devil May Cry
Devil May Cry 3
Diablo 2
Diablo II: Lord of Destruction
Disgaea 2: Cursed Memories
Disgaea: Hour of Darkness
DoDonPachi DaiOuJou
Donkey Kong: Jungle Beat
Doom 3
Dragon Ball Z: Budokai 2
Dragon Ball Z: Budokai Tenkaichi 2
Dragon Quest VIII: Journey of the Cursed King
Dreamfall: The Longest Journey
Drill Dozer
Dynasty Warriors 3
Elemental Gimmick Gear
Enclave
Engacho!
Escape from Monkey Island
Eternal Darkness: Sanity's Requiem
Europa Universalis II
EVE Online
Ever 17: The Out of Infinity
Everquest: The Ruins of Kunark
Everybody's Golf
F-Zero GX
Fable
Fahrenheit
Fallout Tactics
Fatal Frame
Fatal Frame II: Crimson Butterfly
Fate/Stay Night
FEAR
FIFA 2001
Final Fantasy Crystal Chronicles
Final Fantasy Tactics Advance
Final Fantasy X
Final Fantasy X-2
Final Fantasy XI Online
Final Fantasy XII
Fire Emblem
Fire Emblem: Path of Radiance
Fire Emblem: The Binding Blade
Fire Emblem: The Sacred Stones
Fire Pro Wrestling D
Freedom Fighters
Freelancer
Gitaroo Man
Gladius
Goblin Commander: Unleash the Horde
God Hand
God of War
God of War 2
Godzilla: Destroy All Monsters Melee
Golden Sun
Golden Sun 2: The Lost Age
Gothic
Gothic II
Gradius V
Gran Turismo 3: A-Spec
Gran Turismo 4
Grand Theft Auto III
Grand Theft Auto: San Andreas
Grand Theft Auto: Vice City
Grandia II
GrimGrimoire
Guild Wars: Prophecies
Guilty Gear XX
Guitar Hero
Guitar Hero II
Guitar Hero III: Legends of Rock
Gun
Gundam Side Story 0079: Rise from the Ashes
Gunvalkyrie
Half-Life 2
Halo 2
Halo: Combat Evolved
Harvest Moon: Friends of Mineral Town
Heroes of Might and Magic 3: Complete
Hitman 2: Silent Assassin
Hitman: Blood Money
Hitman: Contracts
Homeworld 2
Homeworld: Cataclysm
Hot Shots Golf 3
Hot Shots Golf Fore!
I-Ninja
Icewind Dale
Ico
Ikaruga
In the Groove 2
Incredible Hulk: Ultimate Destruction
Insaniquarium Deluxe
Jade Empire
Jak 3
Jak and Daxter: The Precursor Legacy
Jak II
James Bond 007: Everything or Nothing
Jet Grind Radio
Jet Set Radio Future
Joint Operations: Typhoon Rising
Jurassic Park: Operation Genesis
Katamari Damacy
Ketsui Kizuna Jigoku Tachi
Killer7
King of Fighters 2000
King of Fighters XI
King's Field: The Ancient City
Kingdom Hearts
Kingdom Hearts II
Kirby Air Ride
Kirby: Nightmare in Dream Land
Klonoa 2: Lunatea's Veil
Kohan: Immortal Sovereigns
Legacy of Kain: Defiance
Legacy of Kain: Soul Reaver
Legacy of Kain: Soul Reaver 2
Luigi's Mansion
Mafia: The City of Lost Heaven
Majesty
Mana Khemia 2
Mario & Luigi: Superstar Saga
Mario Kart: Double Dash!!
Mario Kart: Super Circuit
Mario Party 5
Mario Power Tennis
Marvel vs. Capcom 2
Max Payne
Max Payne 2: The Fall of Max Payne
Maximo
Mazan: Flash of the Blade
MDK 2
Mech Assault
Medal of Honor: Allied Assault
Medal of Honor: Frontline
Medieval: Total War
Mega Man Battle Network 2
Mega Man Zero
Mega Man Zero 2
Mercenaries
Metal Gear Solid 2
Metal Gear Solid 3
Metal Gear Solid: The Twin Snakes
Metroid Fusion
Metroid Prime
Metroid Prime 2: Echoes
Metroid: Zero Mission
Midnight Club 3
Midway Arcade Treasures
Mortal Kombat: Deadly Alliance
Mortal Kombat: Deception
Mother 3
Mr. Mosquito
NBA Street
NBA Street Volume 2
NBA Street 3
Need for Speed Underground
Need for Speed Underground 2
NeoGeo Battle Coliseum
Neverwinter Nights
Neverwinter Nights: Horse of the Underdark
Nexus: The Jupiter Incident
NFL 2K1
NFL 2K5
NFL Street 2
NHL Hitz Pro
Ninja Five-O
Ninja Gaiden
No One Lives Forever
No One Lives Forever 2
Oddworld: Stranger's Wrath
Odin Sphere
Okami
Onimusha 2
Onimusha 3: Demon Siege
Onimusha Warlords
Operation Flashpoint: Cold War Crisis
Otogi 2: Immortal Warriors
Otogi: Myth of Demons
Outrun 2
Outrun 2006
Painkiller: On the Flip Side
Panzer Dragoon Orta
Paper Mario: The Thousand-Year Door
Persona 3
Persona 4
Peter Jackson's King Kong: The Game Based on the Movie
Phantasy Star Online
Phantasy Star Online Episode I & II
Phantasy Star Online: Blue Burst
Phantom Dust
Pikmin
Pikmin 2
Pinball Hall of Fame: The Willimas Collection
Pirates of the Caribbean
Pirates!
PlanetSide
Pokemon Ruby/Sapphire/Emerald
Pokemon XD: Gale of Darkness
Postal 2
Power Stone
Power Stone 2
Prince of Persia: The Sands of Time
Prince of Persia: The Two Thrones
Prince of Persia: Warrior Within
Pro Evolution Soccer 2
Pro Evolution Soccer 3
Pro Evolution Soccer 5
Pro Evolution Soccer 6
Pro Pinball Trilogy
Project Gotham Racing
Project Gotham Racing 2
Psychonauts
Puzzle Bobble 4
Quake 3
Rage of the Dragons
Ragnarok Online
Rallisport Challenge 2
Ratchet & Clank
Ratchet & Clank: Going Commando
Ratchet & Clank: Up Your Arsenal
Rayman 2: The Great Escape
Ready to Rumble Boxing
Red Dead Revolver
Remember 11: The End of Infinity
Resident Evil
Resident Evil 0
Resident Evil 4
Resident Evil: Code Veronica
Return to Castle Wolfenstein
Rez
Rhythm Tengoku
Rise of Nations
Rise of Nations: Thrones and Patriots
Robotic Alchmeic Drive
Rogue Galaxy
Rollercoaster Tycoon 2
Rollercoaster Tycoon 3
Rome: Total War
Rune
Sakura Wars 3
Sakura Wars 5: So Long, My Love
Sakura Wars: Atsuk Chishio Ni
Seaman
Serious Sam
Serious Sam: The Second Encounter
Shadow Hearts
Shadow Hearts: Covenant
Shadow of Destiny
Shadow of the Colossus
Shenmue
Shenmue II
Shin Megami Tensei III: Nocturne
Shin Megami Tensei: Digital Devil Saga
Shin megami tensei: Digital Devil Saga 2
Shinobi
Shinobido
Shogun: Total War
Silent Hill 2
Silent Hill 3
Silent Hill 4: The Room
Silent Storm
Sim City 4
Siren 2
Skies of Arcadia
Sly 2: Band of Thieves
Sly 3: Honor Among Thieves
Sly Cooper the Thievious Racoonus
Slyder Adventures
SOCOM II: US Navy SEALs
SOCOM: US Navy SEALs
Sonic Advance
Sonic Adventure 2
Soul Calibur
Soul Calibur 2
Soul Calibur 3
Space Channel 5 Part 2
Spider-Man 2
Splinter Cell
Splinter Cell: Chaos Theory
Splinter Cell: Pandora Tomorrow
SSX
SSX 3
SSX Tricky
Star Wars Battlefront 2
Star Wars Galaxies
Star Wars Jedi Knight II: Jedi Outcast
Star Wars Jedi Knight: Jedi Academy
Star Wars Knights of the Old Republic II: The Sith Lords
Star Wars Republic Commando
Star Wars Rogue Squadron II: Rogue Leader
Star Wars: Battlefront
Star Wars: Empire at War
Star Wars: Knights of the Old Republic
Steambot Chronicles
Street Fighter III: Third Strike
Street Hoops
Stubbs the Zombie in Rebel Without a Pulse
Suikoden III
Suikoden V
Super Mario Advance 4: Super Mario Bros. 3
Super Mario Strikers
Super Mario Sunshine
Super Monkey Ball
Super Monkey Ball 2
Super Smash Bros. Melee
SWAT 4
Sword of the Berserk: Guts' Rage
Syberia
Syberia II
Tactical Ops
Tactics Ogre: Knight of Lodis
Tak 2: The Staff of Dreams
Tales of Symphonia
Tech Romancer
Tekken 4
Tekken 5
Tekken Tag Tournament
Tetris: The Grand Master 3: Terror Instinct
The Chronicles of Riddick: Escape from Butcher Bay
The Elder Scrolls III: Morrowind
The Legend of Zelda: A Link to the Past/Four Swords
The Legend of Zelda: The Minish Cap
The Legend of Zelda: The Wind Waker
The Legend of Zelda: Twilight Princess
The Longest Journey
The Lord of the Rings: The Return of the King
The Simpsons: Hit & Run
The Sims
The Sims 2
The Sims Bustin Out
Thief II: The Metal Age
Tiger Woods PGA Tour 2004
Tiger Woods PGA Tour 2005
Time Crisis 2
Timesplitters 2
Timesplitters: Future Perfect
Tom Clancy's Rainbow Six 3: Raven Shield
Tony Hawk's Pro Skater 2
Tony Hawk's Pro Skater 3
Tony Hawk's Pro Skater 4
Tony Hawk's Underground
Tribes 2
True Crime: Streets of LA
Tsukihimi
Twisted Metal: Black
Ultimate Spider-Man
Unreal Tournament 2004
Vampire The Masquerade: Bloodlines
Viewtiful Joe
Virtua Fighter 4
Virtua Tennis 2
Virtual Pool 3 Featuring: Jeanette Lee
Wacky Races
War of the Monsters
Warcraft 3
Warcraft 3: Frozen Throne
Warhammer 40,000: Dawn of War
Wario Land 4
WarioWare Twisted!
WarioWare, Inc.: Mega Microgames!
Wave Race: Blue Storm
We Love Katamari
Wild Arms 3
Wild Arms 5
Wild Arms Alter Code F
Winning Eleven 8: Final Evolution
Wipeout Fusion
Wolfenstein: Enemy Territory
World of Warcraft
Worms 3D
WWE Smackdown: Here Comes the Pain
WWE Smackdown: Shut Your Mouth
X-Men Legends
Xenosaga Episode I: Der Wille zur Macht
Xenosaga Episode II: Jenseits von Güt und Bosë
Xenosaga Episode III: Also Sprach Zarathustra
XGIII Extreme G Racing
XGRA: Extreme-G Racing Association
Yakuza
Ys: The Oath in Felghana
Zone of the Enders
Zone of the Enders: The 2nd Runner