You can become addicted to anything... alcohol, cigarettes... chess, politics... even exercise, dieting. Addictions are bad! Everything in moderation. :)
I've seen people burn out from playing too much chess, but more often from setting unrealistic goals like "I will gain x elo in y months." We don't control how many rating points we gain, we only control how hard and smart we work at it.
A good friend of mine teaches at one of the schools in my district. He recently told me that he used to be infatuated by chess, but he forced himself to quit it because he was afraid that chess would swallow his life completely, kind of like an alcoholic abstaining from drinking, I guess.
This definitely made me view my own beginning obsession with the game in a new, more worrying light. I was hoping that you all could share any chess burnout stories or your thoughts on being too involved with the game.