Today I played Risk for the first time. It's one of the coolest board games I've ever encountered. (Basically, each player tries to take over the world by strategically conquering territories and continents on a map of Earth.) It appeals to me both on a political and on a logical level.
It's worth noting that my parents nearly broke off their engagement because of a game of Risk that had become particularly intense. From my game today, I can see how that would happen... :-P