I have been playing the most worthwhile game I have ever seen, for about a year now. I cannot do justice to this fantastic game, so try and see for yourself what it is about.
In the west it is called Go, and in the east it has always been a very important past-time. For many people who play professionally, the game is their bread and butter. It is in general a very competitive game, and you get respect for your strength.
Go is played by two players alternately placing black and white stones on the vacant intersections of a 19 × 19 grid board.
The object of the game is to control a larger part of the board than the opponent. To achieve this, players strive to place their stones in such a way that they cannot be captured, while mapping out territories the opponent cannot invade without being captured. A stone or a group of stones is captured and removed if it has no empty adjacent intersections, the result of being completely surrounded by stones of the opposing color.
Please check out http://en.wikipedia.org/wiki/Go_(board_game) .
There is a very active online server called KGS ( www.gokgs.com ) with a nice client, where people of all strengths participate. They will show you how to get started.
You can play everyday for years and years and still there will be people around who are much much stronger than you. It takes a lifetime to master the game and it is very enjoyable.