I'm pretty much in agreement with Big D on this one, gaming is a varied and diverse hobby with varied and diverse enthusists, especially nowadays. When I was very young, and even before my time (which actually seems really bizarre to be) it could be said that a certain game defined a generation of gamers because there were far fewer games, heck far fewer consoles even, than there are now. Perhaps the original did have it's own little section of gamers who praised it above all other games, but I'm quite sure these gamers also had other favorites.

However, I do believe that the concept of gaming itself has gained enough momentum since before the time I could even hold a controller to become sort of a definition of who we are as a society. Our forms of entertainment have evolved into real works of art, in many cases, with intricate plot lines and touching music to name off two of several instances. I don't think Final Fantasy by itself defined a generation, but I think it is a very substantial part of all forms of video gaming, which certainly has it's part in the definitions of the past couple of generations.