FF X and Mario 64.
FF X- Still my favorite RPG, I dunno it just clicked so perfectly at the time and nothing has clicked as well since. Sure it had its flaws just like everything else in life, but I still consider it the best game I've played. First game I cared about the characters enough to say that it actually effected me personally. Took a really cliche story repeated many times (saving the world, the girl, the guy and whatnot) and perfected it.
Mario 64: The first real 3D game I played, the first game that gave a player an open world. So many great games since have also had open worlds but this was the first for me and so it left a huge impression. Everything from GTA to Shadow of the Colossus now owes the realistic 3D open world in console games to this game.
Shadow of the Colossus, Ico and Okami get honorable mentions for being both art and game and so they were all amazing experiences.
GTA 3 for being the first game that really directed the player away from the usual ideas of linear questing and objectives by having a world that can be played endlessly with no objectives and still be good.
Thanks to Blacksaber for the sig!
