Monopoly and Risk are classics, but they're not very well designed. Monopoly relies on people negotiating, and if they don't it lasts way too long, plus a game where losers gets knocked out early isn't as fun. Risk is uneven in that the people who most enjoy it are the ones who've figured out the math and just mercilessly crush their opponents.
I really like Talisman. It calls itself a fantasy quest board game, where each person plays a different type of medieval-fantasy-ish character (the Warrior, the Wizard, the Ghoul, and so on) competing to complete a quest. Easy to learn and fun to play. The downside is that it's expensive (especially if you start buying all of the expansions) but I enjoy the storytelling and adventure aspects of it, and games rarely repeat.
http://en.wikipedia.org/wiki/Talisman_(board_game) (You'll want the fourth edition.)