Not really to do with learning Japanese, but Go is part of Japanese culture. This is an absorbing game with rules simple enough to be grasped in 30 mins but with strategy complex enough to last a lifetime. It is also the only game I’ve come across with a handicapping system that can give an enjoyable and challenging game for both opponents when one is experienced and the other is a novice.
Goban is a mac implementation of GNU Go. It is very elegant and much more convenient sometimes that getting out the board and stones. You can play against the program, or use it to play against opponents locally, on the internet or on your LAN.
If you like chess or strategic games I’d recommend you give Go a try.