Puerto Rico is the best of the dozens of good modern board games that I've played. That or Race for the Galaxy which is similar but with cards.
I also like Kingsburg, which is unusual since it has so many dice yet surprisingly little luck as a result.
Alhambra is a good, slightly easier, game that I save for people newer to board games, and they always enjoy it.
I've really enjoyed Power Grid the couple of times I've played that, despite the fact we got the rules wrong a bit.
For a few more players, Bohnanza (bean trading card game) and Perudo (poker-like dice game) are very popular with a couple of different groups of friends.
San Marco, sadly out of print, is the prettiest game I've got, and is great for three people, though takes a while.
And for Pandemic is great with my family who don't like competitive games, since it's a co-operative one where you all team together to try to beat the game (ie save the world).
All these and far more, along with pictures, reviews and more, can be found at:
www.boardgamegeek.comwhich is an excellent site for any board-game fan.
