2005
Civilization IV
Devil May Cry 3
F.E.A.R.
Ninja Gaiden Black (enhanced version of the 2004 game)
Psychonauts
Rome: Total War - Barbarian Invasion (much better than the base game)
Honorable mentions: Age of Empires III, Condemned: Criminal Origins (melee is good, but the hitboxes are strange, the investigation is very shallow gameplaywise, F.E.A.R. is a much better game), Fahrenheit (I found its first half interesting back in the day, but it aged very badly, and I barely bear QTE-fests now), God of War, Ratchet: Gladiator, Samorost 2, Shadowgrounds, Sly 3: Honor Among Thieves.
2006
Call of Juarez
Company of Heroes
Final Fantasy XII
FlatOut 2 (my all-time favourite racing game besides Carmageddon)
Heroes of Might and Magic V
Okami
Tom Clancy's Rainbow Six: Vegas (yes, popamole RS, but it was immense fun in co-op)
WH40k: Dawn of War - Dark Crusade
Honorable mentions: Dark Messiah of Might and Magic, Medieval II: Total War, Shadow of the Colossus (special game, but I'm not a fun of it), Daxter (I adore Precursor Legacy), The Blackwell Legacy
2007
Civilization IV: Beyond the Sword (really great expansion)
Fantasy Wars
FlatOut: Ultimate Carnage (enhanced version with some extra content, but its great, but I like the original more)
God of War II (my favourite entry of the series)
Portal
Ratchet & Clank: Tools of Destruction (its decline if we compare it to Up Your Arsenal, but it is still a good game, and has Mr. Zurkon)
Sam & Max Save the World
The Darkness
The Witcher
Honorable mentions: Crysis (okayish FPS with great graphics and physics, and it has some freedom and vehicles), Mass Effect (poapamole shooter RPG, but has moments), S.T.A.L.K.E.R. (I didn't played it too much), Uncharted: Drake's Fortune (I liked its vibe, it was more enjoyable than modern Tomb Raiders)
2008
Army of Two (co-op focused fun)
Battlefield: Bad Company (not a remarkable shooter, but it has a great Kelly's Heroes meets Deadly Dozen vibe)
Braid
Sid Meier's Civilization IV: Colonization (servicable, moddable remake of the classic)
Dead Space
King's Bounty: The Legend
Mirror's Edge
Honorable mentions: Ratchet & Clank: Quest for Booty, Spectromancer, Stranglehold.
2009
Batman: Arkham Asylum
Bayonetta
Demon's Souls (not a fan, but I appreciate it despite its faults)
Dragon Age: Origins
King's Bounty: Armoured Princess
Risen
Honorable mentions: Brütal Legend (gameplaywise it's not good, but it is a enjoyable metal comedy tale), Machinarium, Trine, WH40k: Dawn of War II.