When I went to the swedish equivalent of high school one has to choose some kind of direction for one's studies, and you choose a program and a school with this program.
My program was called "Gamer" which in actually was a rather falsely named program, it was a program where you studied programming, graphics and over all game design and development, along with some more common and basic classes such as Math, history and languages, but I think you can see how this program just by merit of it's name attracted "gamer"-people.
Most of us had previously been rather lonely about our passion and all had our own idea of what a "Gamer" was, but when there were so many of us with a rather, figuratively speaking, big sign saying "I AM A GAMER!" the definition of "Gamer" had to be redesigned and this caused many of us to actually discuss the question of "what is a gamer?".
So there are abou 60 "gamer"-students and all of them very different from each other, some had pretty much only played WoW and considered that as more than enough if you took it seriously. We had some that pretty much had dedicated their lives to a game so that they actually made profit form their gaming, they were hardcore and pro sure, but did the "gamer" title really require that much?
We had girls, we had boys, we had black and white, homos and hetros and even a transvestite.
We had FPS-fans, J-fans, console-fans, PC-fans and a schizophrenic.
Even though all the differences, all of these people were in one way or another dedicate to Games, so first we thought "Dedication! That must be it!"
So with that conclusion we started hating upon everyone who didn't seem dedicated enough. But then some of us realized that it was a rather silly definition, because who am I to measure someone elses love and dedication for their games, so back at square one, back to pondering this definition we all thought applied to ourselves, yet didn't really know how.
To make a long story short(er), for it took several years to come to any conclusion, but gamer is a very self adressed "title" if it can even be called as such, a "Gamer" games and has enough love for it to consider themselves "Gamers", just as there are fantasts and terms for those in many areas of media and entertainment.
Btw, the time I spent with these peolpe was glorious! I feel happy with my choice of program just because of all the wonderful "gamers" I got to know there =P