At the weekend I acquired the "Explorers and Pirates"* expansion for "Settlers of Catan". This is an add-on to the original board game.
Catan, as mentioned upthread, is a very simple premise in which dice rolls generate "resources", resources can be used to build more settlements, and the player who gets the most settlements/roads etc by a certain point is declared the winner.
However, the original game can suffer badly from Early Loser Syndrome - the moment when you're sitting there with the perfect set of resources, just waiting for someone to roll an eight to get that brick you need and really start building, and four turns later you're still sitting there waiting for someone to roll that eight and everyone else is building their fourth city... You can trade cards with other players, but if no-one's got what you need at a trade price you can afford, or if there are only two players, it never really works.
Pirates and Explorers introduces a bank! Any time that a roll doesn't give you a resource, you get one gold, and with two gold you can
buy a resource! This really helps prevent any initial bad rolls from being magnified. The bank also trades at a fixed price, so suddenly trading in a two-player game starts to happen again, as one player tries to undercut the bank.
P&E also introduces ships, seafaring exploration, pirates, and overseas resources. The downside is that the game is far more complex than the original version (you have to learn how ships move, consider how to ferry settlers and troops across the sea, overcome pirate dens with heroic feats of derring-do and statistics). As a result, the games booklet is one of those which gives me a sinking feeling when I try and read it (I couldn't even comprehend step 1, which was to sort all the counters into bags as instructed). It contains "scenarios" - so the first one is "Exploring", to enable the players to understand how ships move and new land is discovered. The second is "Pirates", and the players learn about carrying troops in their ships and Missions (fighting Pirates in this case). The next tutorials are on Fishing and Spice trading, and only then do you know enough to play the full game (I only got the game at the weekend, so I'm not there yet).
In summary, I think this seems a more balanced and nuanced game, but at a cost of becoming more complex and harder for a novice to pick up over a pint of beer.
*Everything's better with Pirates!
