I second the recommendation for Carcassonne, and to not start with expansions - excepting perhaps the mini-expansions The River or The River II, as they make for a more interesting start without otherwise affecting the rules. Puerto Rico - http://www.boardgamegeek.com/game/3076 - is also worthwhile - has a long setup time, a slow build up, and far too many tokens - but it all pays off in the end game (much more so than I'd expected).
A two player game which I can highly recommend is Yinsh - http://www.boardgamegeek.com/game/7854 . This gets mindbendingly fun (in an "ouch, my brain hurts, but I _think_ that you can't stop me if I do _this_ *evil laughter*" kind of way) after the first couple of games when you grok some basic strategy. For 4 players, just bring two sets of Yinsh and rotate opponents after each game. (Or try one of the five other Project Gipf games; though imo Yinsh is the most rewarding of them all.)
Oh, and peruse the archives of Hixie's weblog - he's the boardgame master, and has many recommendations.