While there are various other outliers such as TD view Zelda-likes and ARPGs, I've focused on 2D sidescrollers (and later TP view platformers) here. See my worlds unraveled site for info on games in other perspectives.  

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2002:

Mega Man Zero (GBA, 2002)
Star Fox Adventures (GC, 2002)? - WIP
Ape Escape 2 (PS2, 2002)? - WIP
Super Mario Sunshine (GC, 2002) - WIP
Star Wars Jedi Knight II: Jedi Outcast (Multi, 2002)? - WIP
Sly Cooper and the Thievius Raccoonus (PS2, 2002) - WIP
Grand Theft Auto: Vice City (Multi, 2002)? - WIP
Densetsu no Starfy GBA, 2002) - WIP
Disaster Report (PS2, 2002)? - WIP

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2003:

Gothic II: Night of the Raven (PC, 2003)(Expansion)?
MapleStory (PC, 2003)?
Ys VI: The Ark of Napishtim (PC, 2003/PS2, 2005)
Legacy of Kain: Defiance (Multi, 2003)
Deus Ex: Invisible War (PC/XB, 2003)?
Tron 2.0 (PC, 2003(XB, 2004)
Sword of Mana (GBA, 2003)(Seiken Densetsu/Final Fantasy Adventure remake)
Prince of Persia: The Sands of Time (Multi, 2003) 
Primal (PS2, 2003)? 
Ghosthunter (PS2, 2003) 
Castlevania: Lament of Innocence (PS2, 2003)
Mega Man Network Transmission (GC, 2003)?
Seiklus (PC, 2003)
Tenchu: Wrath of Heaven (PS2, 2003)?
Summon Night: Swordcraft Story (GBA, 2003)
Rockman EXE WS (WS, 2003)?
Mario & Luigi: Superstar Saga (GBA, 2003) 
Jak II (PS2, 2003)

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2004: 

Vampire: The Masquerade - Bloodlines (PC, 2004)

Sly 2: Band of Thieves (PS2, 2004)? - WIP
The Legend of Zelda: The Minish Cap (GBA, 2004) 
The Legend of Zelda: Four Swords Adventures (GC, 2004) 
Atelier Iris: Eternal Mana (PS2, 2004) 
Paper Mario: The Thousand Year Door (GC, 2004) 
Blood Will Tell (PS2, 2004) 
Gurumin: A Monstrous Adventure (PC, 2004/PSP, 2007) 
Super Mario 64 DS (NDS, 2004) 
X-Men Legends (Multi, 2004) 
Prince of Persia: Warrior Within (Multi, 2004)?
Jak 3 (PS2, 2004)?
Forgotten Realms: Demon Stone (PS2/PC/XB, 2004) 
Second Sight (Multi, 2004/PC, 2005) 
Onimusha 3: Demon Siege (PS2, 2004/PC, 2005) 
Thief: Deadly Shadows (PC/XB, 2004)
Baldur's Gate: Dark Alliance II (PS2/XB, 2004) 
Grand Theft Auto: San Andreas (PS2, 2004/PC/XB, 2005) 
A.I.M. (Artificial Intelligence Machine)(PC, 2004)?
Ninja Gaiden (XB, 2004/PS3, 2007)
Breakdown (XB, 2004) 
Tales of Rebirth (PS2, 2004)(Untranslated) 
Tom Clancy's Splinter Cell Pandora Tomorrow (Multi, 2004) 
Operation Shadow (N-Gage, 2004)?
Tenchu: Fatal Shadows (PS2, 2004) 
The Incredibles (Multi, 2004) 
The Suffering (PC/XB/PS2, 2004) 
City of Heroes (PC, 2004) 
World of Warcraft (PC, 2004)
EverQuest II (PC, 2004) 
Monster Hunter (PS2, 2004/PSP, 2005 (Remix)) 

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2005

Kingdom Hearts II (PS2, 2005)?

Ty the Tasmanian Tiger 3: Night of the Quinkan (Multi, 2005)?
Mercenaries: Playground of Destruction (XB/PS2, 2005)

Extra Mario Bros. (PC, 2005)(NES Rom Hack)

Dragon Quest Heroes: Rocket Slime (NDS, 2005)

Atelier Iris 2: The Azoth of Destiny (PS2, 2005)

Steambot Chronicles (PS2, 2005)?
Summon Night EX-Thesis: Yoake no Tsubasa (PS2, 2005)(Untranslated)?
X-Men Legends II: Rise of Apocalypse (Multi, 2005)

Mario & Luigi: Partners in Time (NDS, 2005)

​Prince of Persia: The Two Thrones (Multi, 2005) 
LEGO Star Wars (Multi, 2005) 
Devil May Cry 3 (PS2, 2005/PC, 2006) 
God of War (PS2, 2005) 
​Oddworld: Stranger's Wrath (XB, 2005/Multi, 2010) 
​Shinobido: Way of the Ninja/Shinobido Imashime (PS2, 2005) 
Shadow of the Colossus (PS2, 2005)

Ninja Gaiden Black (XB, 2005)(Includes the prequel)?
Xanadu Next (PC, 2005) 
Sigma Star Saga (GBA, 2005) 
Stubbs the Zombie in Rebel Without a Pulse (PC/XB, 2005) 

Resident Evil 4 (Multi, 2005)

Killer7/Killer 7 (GC/PC/PS2, 2005) 
Grand Theft Auto: Liberty City Stories (PSP, 2005/PS2, 2006) 
Rogue Galaxy (PS2, 2005) 
Tom Clancy's Splinter Cell: Chaos Theory (Multi, 2005) 
Hi Hi Puffy AmiYumi: Kaznapped! (GBA, 2005) 

Yakuza (PS2, 2005/PS4, 2017 (Yakuza Kiwami)) 
Call of Cthulhu: Dark Corners of the Earth (XB, 2005/PC, 2006) 
Genji: Dawn of the Samurai (PS2, 2005) 
Peter Jackson's King Kong: The Official Game of the Movie (Multi, 2005) 

Hello Kitty: Roller Rescue (Multi, 2005) 

Spartan: Total Warrior (XB/GC/PS2, 2005) 
City of Villains (PC, 2005) 
Digimon World 4 (XB/GC/PS2, 2005) 
Dungeon Lords (PC, 2005)
Space Cowboy Online (PC, 2005)?
Fullmetal Alchemist 3: Kami o Tsugu Shoujo (PS2, 2005)(Untranslated) 

​

2006

Ys Origin (PC, 2006/Multi, 2017)?

The Elder Scrolls IV: Oblivion & Knights of the Nine DLC pack (PC/XB360, 2006/PC, 2007)?
Forbidden Siren 2 (PS2, 2006)?
Gothic 3 (PC, 2006)?
Dark Messiah of Might and Magic (PC/XB360, 2006)?
Valkyrie Profile 2: Silmeria (PS2, 2006)
LaTale (PC, 2006)
LEGO Star Wars II: The Original Trilogy (Multi, 2006)
Raw Danger!/Zettaizetsumei Toshi 2 (PS2, 2006)?
Bully (PS2, 2006/PC/Wii/XB360, 2008)
Tomb Raider: Legend (Multi, 2006)
Atelier Iris 3: Grand Phantasm (PS2, 2006)
Valkyrie Profile: Lenneth (PSP, 2006)(Remaster of the PS1 game)?
Destroy All Humans! 2 (XB/PS2, 2006)
Wild ARMs 5 (PS2, 2006)
Tom Clancy's Splinter Cell: Double Agent (Multi, 2006) 
Hitman: Blood Money (PC/PS2/XB, 2006) 
Grand Theft Auto: Vice City Stories (PSP, 2006/PS2, 2007) 
Yakuza 2 (PS2, 2006) 
Scarface: The World Is Yours (Multi, 2006/Wii, 2007) 
Dead Rising (XB360, 2006) 
The Godfather (Multi, 2006) 
Monster House (GBA, 2006)
​Marvel: Ultimate Alliance (Multi, 2006)
Ys V: Lost Kefin, Kingdom of Sand (PS2, 2006)(Remake) 
ROBLOX (PC, 2006) 
Rengoku II: The Stairway to H.E.A.V.E.N. (PSP, 2006)?
Saints Row (XB360, 2006) 
Monster Hunter 2 (PS2, 2006)(semi-fan translated) 
Baten Kaitos Origins (GC, 2006) 
Tales of Destiny (PS2, 2006)(Remake, untranslated)? 
Ace Online (PC, 2006) 
Veggie Tales: LarryBoy and the Bad Apple (GBA, 2006) 
Wai Wai World (Mobile, 2006)(NES port/remix) 
Painajainen (PC, 2006) 
Knytt (PC, 2006) 
Akumajo Dracula Special: Boku Dracula-kun or "Devil's Castle Special: Kid Dracula" (Mobile, 2006)(NES port?)?
Ar tonelico: Melody of Elemia (PS2, 2006) 
Brave Story (PS2/DS, 2006)(Untranslated, not the same as New Traveler for PSP) 
EverQuest II: Echoes of Faydwer (PC, 2006)(Expansion) 
Blue Dragon (XB360, 2006)

​

2007

BioShock (PC/XB360, 2007/Multi, 2008)?

​Ratchet & Clank Future: Tools of Destruction (PS3, 2007)? - TPS

Art of Theft (PC 2007)? - Level-based stealth game?
Konami WaiWai Sokoban (Mobile 2007)?
​​​Assassin's Creed (Multi, 2007)?

 

AA:
​​God of War II (PS2, 2007)
Uncharted: Drake's Fortune (PS3, 2007)
The Godfather: Blackhand Edition (WII, 2007)
Tomb Raider: Anniversary (PS2/PC/XB360, 2007)
Ninja Gaiden Sigma (PS3, 2007)
The Godfather: The Don's Edition (PS3, 2007)
The Legend of Zelda: Phantom Hourglass (DS, 2007)
Tomb Raider: Anniversary (PSP, 2007)
Grand Theft Auto: Vice City Stories (PS2, 2007)
I Wanna Be the Guy: The Movie: The Game (PC, 2007)
Chibi-Robo! Park Patrol (DS, 2007)
Manhunt 2 (PSP, 2007)
Metal Gear Solid: Portable Ops Plus (PSP, 2007)
Folklore (PS3, 2007)
Silent Hill: Origins (PSP, 2007)
Lost in Blue 2 (DS, 2007)
Penumbra: Overture (PC, 2007)
Overlord (PC/XB360, 2007)
Crackdown (XB360, 2007)
Lost in Blue 3 (DS, 2007)
Prince of Persia Rival Swords (PSP, 2007)

 

ARPG:
The World Ends with You (DS, 2007)
Monster Hunter Freedom 2 (PSP, 2007)
Crisis Core: Final Fantasy VII (PSP, 2007)
.hack//G.U. vol. 3//Redemption (PS2, 2007)
Mega Man Star Force 2: Zerker x Ninja (DS, 2007)
Mega Man Star Force 2: Zerker x Saurian (DS, 2007)
Odin Sphere (PS2, 2007)
Star Ocean: First Departure (PSP, 2007)
Tales of Destiny 2 (PSP, 2007)
Super Paper Mario (WII, 2007)
Titan Quest: Gold Edition (PC, 2007) & Titan Quest: Immortal Throne (PC, 2007)(Expansion)
Jade Empire: Special Edition (PC, 2007)
The Witcher (PC, 2007)
Summon Night: Twin Age (DS, 2007)
Shining Force EXA (PS2, 2007)
Tales of Innocence (DS, 2007)
Phantasy Star Universe: Ambition of the Illuminus (PS2, 2007)

​

2008

Kung Fu Panda (Multi, 2008)?
​Bionic Commando: Rearmed (Multi, 2008)? - WIP

Super Smash Bros. Brawl (Wii, 2008)? - "The Great Maze" level in “The Subspace Emissary” mod
Dead Space (Multi, 2008)
Iji (PC, 2008/v1.7, 2017) - Action Platformer w/ RPG elements
Banjo-Kazooie: Nuts & Bolts (XB360, 2008)? - 3D, mini-game/challenge focused
Soul of Darkness (Mobile 2008/DSiWare)? - WIP

Check GameFAQs​
 

2009
The Legend of Zelda: Spirit Tracks (DS, 2009)?
A Boy and His Blob (Wii, 2009/Multi, 2016)? - Puzzle
Legend of Princess (PC, 2009) - Demo only (one dungeon), Zelda clone fan game by the Iconoclasts developer
Trine (PC, 2009)? - Puzzle/ARPG?, 2-player coop
Koumajou Densetsu Scarlet Symphony (PC, 2009)?
GuitarFreaks & DrumMania V6 (Arcade 2009)? - Probably a joke