This is so freaking hard, because

1996
Resident Evil - PSX, 1996
The Logical Journey of the Zoombinis - PC, 1996
Mario Kart 64 - N64, 1996
Civilization II - PC, 1996
Crash Bandicoot - PSX, 1996
Pokémon Red & Blue (JP release)

1997
Final Fantasy VII - PSX, 1997
Age of Empires - PC, 1997
GoldenEye 007 - N64, 1997
Grandia - PSX, 1997
Alundra - PSX, 1997
Worms 2 - PC, 1997
Crash Bandicoot 2 - PSX, 1997

1999
The Longest Journey - PC, 1999
Final Fantasy VIII - PSX, 1999
Warzone 2100 - PSX, 1999
Sid Meier's Alpha Centauri - PC, 1999
Pokémon Red & Blue (PAL release)

2002
Warcraft III - PC, 2002
The Mark of Kri - PS2, 2002
The Elder Scrolls III: Morrowind - PC, 2002
Gothic II - PC, 2002
TimeSplitters 2 - PS2, 2002

2006
Slaves to Armok: God of Blood Chapter II: Dwarf Fortress - PC, 2006
Dreamfall: The Longest Journey - PC, 2006
Final Fantasy XII - PS2, 2006
Resistance: Fall of Man - PS3, 2006
The Elder Scrolls IV: Oblivion - PC, 2006

2007
Mass Effect - 360, 2007
Uncharted: Drake's Fortune - PS3, 2007
Halo 3 - 360, 2007
Crisis Core: Final Fantasy VII - PSP, 2007
Crysis - PC, 2007
Lost Odyssey - 360, 2007

2009
Uncharted 2: Among Thieves - PS3, 2009
Flower - PS3, 2009
Final Fantasy XIII - PS3, 2009
Batman: Arkham Asylum - PS3, 2009
The Sims 3 - PC, 2009
Football Manager 2010 - PC, 2009

2012
Far Cry 3 - PS3, 2012
Journey - PS3, 2012
Frog Fractions - PC, 2012
XCOM: Enemy Unknown - PC, 2012
Mass Effect 3 - 360, 2012
Deus Ex: Human Revolution - PS3, 2012

Weirdly, and to my surprise, I'm thinking 1999 or 2012 might edge it. 2007's a good shout, too. It surprises me particularly how few of my absolute favourite games came out in a single year in the mid-90's. However, overall, 1996-2001 remains the most consistently awesome period of gaming for me.