Yahtzee makes an interesting point about the word "gamer" and the marketing of gaming (t-shirts, etc.).
I don't necessarily agree. I don't think anything is wrong about calling yourself a "gamer". Not as a definition of yourself, but as an adjective describing just one of your facets.
edit: summary: "I'm not saying you have to be ashamed of playing videogames, but I'm not saying you should be proud and shouting it from the rooftops either. It's not like being a gay vicar or a female boxer or a quadruple amputee ping pong champion. Being a player of games does not make one a minority or part of an elite club, as employing a label like "gamer" wordlessly implies."