Wow, I'm amazed there aren't that many Euro/designer gamers amongst this lot. While Monopoly and Risk, etc, certainly have nostalgic charm... I would be very hard pressed to call them good (after discovering the "new" generation of boardgames).
My current favorite games:
Hammer of the Scots : One of the ultimate wargames ever created. Great tactical depth, clean rules, 2 to 3 hour play-time. And, my gawd, the blocks are too damned cool.
Memoir '44 : Clean rules, short playtime, tons of fun. If you like/love Risk, Axis & Allies, Fortress America, Shogun, etc, you absolutely have to have this game. It is wicked fun.
Europe Engulfed : When it comes to "grand strategy" WWII games, you'd be hard pressed to beat this title. Granted there are much more detailed simulations, but you're also looking at upwards of 60+ hours to finish. EE gives all the detail and historical flavor, without bogging you down in pedantic rules. The full campaign can be completed in 14 to 24 hours (depending on your experience). Shorter scenarios can be completed in 2 to 4.
Vinci : Quick civ/empire building game. Supports up to 6 players. Usual play-time is about 2 hours (give or take). The combination of civ attributes give this a lot of spice and replayability.
Modern Art : A bonified classic.
Union Pacific : Rail-road building, stock manipulation game. While not as intense as the 18xx series, this game is way fun to play.
Napoleon : Another Columbia "block game". Much like Hammer of the Scots, this features great rules and tremendous strategic/tactical depth. As a bonus, you can play with three. Average game is about 2 hours.
Rommel in the Desert: Tense, tense, tense. If you want to learn what it was like to be engaged in Northern Africa, here's your game. It's all about supply and bluff. Scenarios range from 1.5 hours up to 6 (if they go that long).
Honorable mentions to: Princes of the Renaissance, El Grande, Twilight Imperium, Age of Steam, Bang!, Carcassonne, Pirate's Cove, Friedrich, Liberty, Settlers of Catan, Intrige, etc, etc.
Check the link in my .sig for thousands of entertaining boardames that you've never even heard of. Once you play some of these, you'll never go back to Monopoly, Risk, Life, etc. It's hard to believe, but it happened to me.
-V