PS2 was a juggernaut. I'm not sure how anyone could legitimately narrow its library down to only one game being worthy as the absolute best.
Right now I am thinking Final Fantasy X. It came out on 12/17/2001 in the US which made it perhaps the best video game (as in software) gift I ever got during the holiday season. Also, playing a new Final Fantasy at that time of year back then was just magical.
Tomorrow my favorite could be Katamari Damacy, SSX, GTA3, Tekken Tag Tournament, MGS2 (or 3), Dragon Quest VIII, Valkyrie Profile 2: Silmeria... there are just so many PS2 games that can be considered GOAT for the console.