My brother-in-law introduced me to games when I was 14. He and my sister lived an hour away, but when I was able to go to their house we'd spend most of our time playing games. He intorduced me to Risk, among other good games. Then, when I was 16, I had a defining moment in my life. I walked to the toy/game store in our small town and found the store had just put on display Avalon Hill games. I spent a week agonizing over whether I should buy D-Day, Guadalcanal, Midway or Afrika Korps. (My dad didn't believe in allowances, so $4 was a lot to me at the time.) I settled on the latter, and my life was changed forever. After a stint in Vietnam (defining my age) I went to college and began to discover other guys who loved war games. The guy who most launched me into real war-gaming was Richard Nixon (just had to say that, but this Nixon worked in the bank in Boulder, CO). While in graduate school a bunch of us put together a gaming group in Denver. Then "real life" came with graduation and I had to move further west to my first "real job." But I was not detered. I met a guy who loved games more than I (yes, it is possible, as proven by the guys on BGG who own hundreds of games - I just don't quite get it) and we discovered a college professor who loved war games, and soon we had a gaming group there, as well. In 2002 my wife and I took a road trip across the country (highly recommended) and crossed the Mississippi at Vicksburg. This was my first visit to a Civil War battlefield. Vicksburg isn't that great, as I've since discovered. But we drove to Chattanooga, Atlanta, Savannah, and finally Richmond, and by the end of that trip I was obsessed with the Civil War. (Now every few years I take another road trip and have been to a LOT of Civil War battlefields.) I have a son-in-law who has introduced me to other great games that are not violence based, and I find I am able to enjoy them as well.
2010 update: The last few years I've found myself playing more and more games outside the wargame genre. I enjoy Agricola, Railroad Tycoon, Thunderstone (too weird for a guy my age, but it IS fun), Year of the Dragon, Dominion, etc. etc. I don't play that many wargames at this time, but I must add, at present the game I'm most obessessed over is Conflict of Heroes: Storms of Steel.