I've been gaming as long as I can remember, and I have a terrible memory... I'll just do this gen by platform...

Nintendo DS

• 2004: Feel the Magic: XY-XX (Sega)
• 2005: Advance Wars: Dual Strike (Nintendo / Intelligent Systems)
• 2006: Dragon Quest Heroes: Rocket Slime (Square Enix/ Tose Software)
• 2007: Etrian Odyssey (Atlus / Lancarse)
• 2008: Castlevania: Order of Ecclesia (Konami)
• 2009: Retro Game Challenge (Xseed / Namco / indiezero)

Xbox 360

• 2005: Geometry Wars: Retro Evolved (MGS / Bizarre Creations)
• 2006: Dead Rising (Capcom)
• 2007: Crackdown (MGS / Realtime Worlds)
• 2008: Tales of Vesperia (Bandai Namco / Tales Studio)
• 2009: Street Fighter IV (Capcom / Dimps)

Wii

• 2006: The Legend of Zelda: Twilight Princess (Nintendo)
• 2007: Super Mario Galaxy (Nintendo)
• 2008: Okami (Capcom / Ready at Dawn Studios)
• 2009: Little King's Story (Xseed / Marvelous / Cing / TownFactory)

I'll edit this post when I get home from school.

As promised. Bracket = runner-up(s)

1994 - Secret of Mana
1995 - Lunar 2 (Phantasy Star IV)
1996 - Civilization II (Tekken 2)
1997 - Age of Empires (Kirby's Dream Land 3)
1998 - Half Life (Parasite Eve)
1999 - Unreal Tournament (Pokemon Red, Heroes of Might & Magic 3)
2000 - Diablo II (Counter-Strike, Pokemon Silver, Legend of Dragoon); Damn, what a year.
2001 - Super Smash Bros. Melee (Grandia)
2002 - Diablo II LoD (Warcraft 3 RoC, Grandia II)
2003 - Warcraft 3 TFT (Skies of Arcadia Legends?)
2004 - Half Life 2 (Unreal Tournament 2004, Rome: Total War)
2005 - World of Warcraft (Fire Emblem: The Sacred Stones)
2006 - Tales of the Abyss (Medieval 2: Total War, Kirby Mouse Attack)
2007 - Metroid Prime 3 (Uncharted: Drake's Fortune, Super Mario Galaxy)
2008 - Super Smash Bros. Brawl (Valkyria Chronicles, Yakuza 2)
2009 - Uncharted 2: Among Thieves (New Super Mario Bros. Wii, Ar tonelico II)
2010 -  Yakuza 3

9 PC
2 Wii
2 PS3
1 SNES
1 GCN
1 PS2
1 Sega CD

Pretty obvious what system I grew up playing the most

Judging by your pictures, the fact that you opened many threads (including official) and your numerous notice, I think you love Final Fantasy.

2006 - Twilight Princess
2007 - Super Mario Galaxy
2008 - Mario Kart Wii
2009 - New Super Mario Bros Wii
2010 - Super Mario Galaxy 2 (sure) or Zelda Wii or Metroid Other M

2000 - Shenmue

2001 - Metal Gear Solid 2: Sons of Liberty

2002 - Silent Hill 2 (pc)

2003 - ??

2004 - Metal Gear Solid 3: Snake Eater

2005 - Resident Evil 4 (ps2)

2006 - Final Fantasy XII

2007 - Uncharted: Drake's Fortune

2008 - Metal Gear Solid 4: Guns of the Patriots

2009 - ? Heavy Rain ? (Bayonetta/Uncharted2/Modern Warfare2)

1996-Super Mario 64
1997-Star Fox 64
1998-Pokemon Red/Blue/Marvel vs. Capcom: Clash of Super Heroes
1999-Super Smash Bros
2000-Marvel vs. Capcom 2: A New Age of Heroes
2001-Super Smash Bros Melee
2002-Super Mario World: Super Mario Advance 2
2003-Pokemon Ruby/Sapphire
2004-Halo 2
2005-Resident Evil 4
2006-Gears of war
2007-Halo 3
2008-Gears of War 2/Mario Kart Wii
2009-Left 4 Dead 2

2007 COD4
2008 MGS4
2009 Dragon Age: Origins

Mine is going to be a bit of a weird mix of years from memory.... and Wikipedia:

1984 Bomb Jack (This was technically released the year before I was born but still brilliant!)
1985 Starquake

1987 Super Mario Bros. (EU release)

1990 Super Mario Bros. 3
1991 Super Mario World (again, both EU releases)
1993 Doom
1994 Tekken
1995 EDIT (how did I forget this?!): Chrono Trigger (2nd place: Rise of the Triad)
1996 Duke Nukem 3D
1997 Final Fantasy VII
1998 Half-Life
1999 Metal Gear Solid (2nd place Age of Empires II, 3rd place Unreal Tournament, 4th place Planescape Torment... what a year!)
2000 Deus Ex (Greatest Game Ever!)
2001 Final Fantasy X
2002 Neverwinter Nights or Age of Mythology
2003 Star Wars Knights of the Old Republic (2nd place CoD)
2004 Half-Life 2
2005 Metal Gear Solid 3 (2nd place to Age of Empires 3)
2006 Elder Scrolls IV: Oblivion
2007 Call of Duty 4: Modern Warfare (2nd place to Orange Box, 3rd to Crysis)
2008 Metal Gear Solid 4
2009 Dragon Age: Origins (2nd place Uncharted 2)
2010 Mass Effect 2... so far

91 - Super Mario World (2nd: Sonic the Hedgehog)
92 - Super Mario Kart (2nd: Sonic the Hedgehog 2)
93 - SimCity 2000 (2nd: The Legend of Zelda: Link's Awakening)
94 - Super Metroid (2nd: Final Fantasy VI)
95 - Chrono Trigger (2nd: Yoshi's Island)
96 - Super Mario 64 (2nd: Super Mario RPG: Legend of the Seven Stars)
97 - GoldenEye 007 (2nd: Mariokart 64)
98 - The Legend of Zelda: Ocarina of Time (2nd: Pokemon Red/Blue)
99 - Pokemon Yellow (2nd: RollerCoaster Tycoon)
00 - The Legend of Zelda: Majora's Mask (2nd: Pokemon Gold/Silver)
01 - Super Smash Bros. Melee (2nd: Golden Sun)
02 - Metroid Prime (2nd: Super Mario Sunshine)
03 - Final Fantasy Tactics Advance (2nd: The Legend of Zelda: The Wind Waker & Fire Emblem)
04 - Golden Sun: The Lost Age (2nd: Metroid Prime 2 Echoes)
05 - Resident Evil 4 (2nd: Castlevania: Dawn of Sorrow)
06 - The Legend of Zelda: Twilight Princess (2nd: Castlevania: Portrait of Ruin)
07 - Super Mario Galaxy (2nd: Metroid Prime 3 Corruption & Fire Emblem: Radiant Dawn)
08 - Super Smash Bros. Brawl (2nd: Dead Space)
09 - Resident Evil 5 (2nd: New Super Mario Bros. Wii)
10 - Monster Hunter Tri (basically cause it's the only game I've played from '10. I expect this to either be Metroid: Other M or Zelda Wii)