Ah, the Settlers of Catan. I first played this board game 9 years ago with my diverse group of stoner friends. When I married my wife 6 years ago I though I would never see Catan again, due to my friends not being allowed in my home. Well now I can play without the slightest chance of grape soda (or bong water) getting on the carpet!
This game is great- it's relaxing and fairly simple. You build settlements, roads and cities by spending resource cards. The main strategic elements are road and settlement placement, but there is a large element of diplomacy as well- You usually have a resource or two that is in short supply and you have to trade some other resources to other players to build what you need.
The pace is slow but that allows you time to strategize! It can also be played without any strategy and due to the luck factor you still have a chance to win. You miss out on some amount of player interaction that you would get face to face over an actual game board, but the benefits more than make up for this- It is cheaper than the 'solid' version, at $10 a great deal for your money, you can't lose the pieces and it keeps track of all the info you could possibly want to know about the game. And it's WAY easier to scrape up some players (always the toughest part of a board game). Even if you don't have an xbox live gold account there are AIs to play against, and on hard difficulty they are pretty tough!
I love games where you build stuff (I am betting they will come out with a 'Rails' game before too long) so I may be biased, but I feel this is the best XBL arcade game put out this year.