For me it was Final Fantasy X and Shenmue. The jump from fifth to sixth generation was so ridiculously massive, I thought I was watching a pre-rendered cutscene at the start of Shenmue! I was always unimpressed with the graphics in the 5th generation, I actually preferred the way most SNES and Megadrive games looked compared to most PS1/N64/Saturn games. Though there was a noticeable improvement on the 2D front that I appreciated.
Later on, Half-Life 2 and Escape From Butcher Bay gave my eyes orgasms, the animations (especially facial animations) and texture quality in Half-Life 2 were completely unmatched at the time and every single light seemed to throw shadows around in Butcher Bay; I remember creeping up on someone in Butcher Bay from a ledge above them, a light behind me, my shadow looming over them ominously. Shit was awesome.
As for this generation, it was Crysis. When you finally leave the forest near the start and the sun is rising I couldn't believe what I was seeing; real-time crepuscular rays. Beams of light were actually streaming through the leaves in real time. I couldn't believe my eyes.