FFX for me. That game was the first in the series released when I was old enough to care. It was the first story driven game I ever played, and I know a lot of fans that had been with the series longer didn't like it but it was the game that opened me up to RPGs other than Pokemon. FFX will always have a place in my heart despite that ungodly awkward laughing scene in Luca.
My first hand was super Mario Kart.
The legend of Zelda orcarina of time was the game that got me interested in gaming.
However it was really the ratchet and clank, Jak, and Battlefront series that cemented me as a gamer.