Miscellany: Puerto Rico
If there's one board game that embodies the Eurogaming scene, it's "Puerto Rico." The game, designed by Andreas Seyfarth, spent a lot of time at the #1 spot at boardgamegeek.com. It was eventually dethroned by farm simulator Agricola, but it's still a good choice if you start to get tired of "Settlers of Catan."
The premise doesn't sound too gripping at first: you play as a plantation owner in the colony of Puerto Rico in the 17th century. During the game, you'll acquire colonists and grow crops; each player chooses a role, takes an action with a special privilege, and then all other players take the same action without the privilege. To get victory points, you either ship crops to the Old World or buy buildings, or both, depending on your strategy.
The fun comes after the first few playthroughs, which will most likely be spent blundering through the poorly written rulebook (translated from the German). The only random element in the game are the plantation tiles that appear, and even those can be predicted (the higher value crops are slightly more rare), so it's very easy to formulate and execute a plan to succeed.
There are a bunch of possibilities. Will you try to ship as much corn as possible to the Old World, using your private ship and warehouses to protect your precious grain? Or maybe you'll become a coffee baron, using the riches from the sales of the crop to fund a massive series of building projects? Perhaps you'll diversify, producing and shipping at opportune times and using the Factory building to increase your production profits?
It's really the buildings that make the whole thing go, since each building allows you to break the rules in various ways. This sort of exception-based design can be very compelling if executed correctly (see "Magic: The Gathering" and "Guilty Gear" for prime examples), so it's no surprise "Puerto Rico" is popular.
[One sidenote - the game's "colonists" are dark brown circular discs, and given the real-life history of Puerto Rico, they should have probably been called "slaves." I don't like it when games whitewash history like this.]