There's a particular type of board game (or card game) that I like to play. It's any game for three to six people that requires a fair amount of skill, but also has a large element of luck. What's nice about these games is that if you are best at them you can enjoy your applications of skill, but the other playrs will not be overly dominated by your ability; they will enjoy the game just as much, and often win. They may not even notice that you are playing the game better than they are.
I just discovered a card game like this called "Kingpro" on my PDA. The old board game of Talisman was an excellent example of this sort. Unfortunately, the game of "Hearts" does not qualify. Someone needs to invent a variation of Hearts that has quite a bit more luck.