I'm confused, you want the "best" game for each year or the game that has been the best since the ps2 was out? And it differs, all sites, publications etc use a different game, there is no universal best...though there are critically acclaimed like metal gear solid, ico, etc.
the only Ps2 game that had won the overall Game of the Year by The Academy of Interactive Science and Art award(the official Awards for gaming,the Oscar of gaming) is God of War in 2005. here is the full list: 1997-Golden Eye(n64) 1998-Legend of Zelda:The Ocarina of time(n64) 1999-The Sims(pc) 2000-Diablo 2(pc) 2001-Halo(x-box) 2002-Battlefied 1942(pc) 2003-Call of Duty(pc) 2004-Half-life 2(pc) 2005-God of War(ps2) 2006-Gears of War(x-box 360) 2007-Call of Duty 4:Modern Warfare(multiplatform) 2008-Little Big Planet(ps3) 2009-Uncharted 2(ps3)