Modular board games allow you to play on a new board each game, because the board is built fresh as you go. This often gives a game greater replayability -- adding to the enjoyment of it. Here's a list of my five favorite modular board games.
Settlers is the first designer game which caught widespread attention in America. (Worldwide, Settlers and its expansions have sold more than 6 million copies.) The changing board layout ensures that every game is different, and there's a fine balance between skill and luck. Several game expansions are available. If you've never played, you owe it to yourself to give it a try.
Players race paddle boats down the Mississippi River, which can take unexpected twists and turns. You must pick up some passengers along the way, also managing your coal supply carefully so you don't run out of fuel and run your boat ashore.
Pirates compete to escape from jail in this game, where you must move forward to get into the boat -- but the only way to move forward is to move backward (picking up resources cards by doing so). Clever and engaging, Cartagena also is deceptively simple.
Although it is now unfortunately out of print, copies of RoboRally can be found on eBay and via other outlets for used games. As players try to move their robots through a series of checkpoints on a factory floor, they're confronted by many obstacles -- some merely annoying, some quite deadly.
Building cities and developing the resources necessary for them to grow will lead to victory in this board game. Exactly how the cities get laid out and where the resources are changes every game.