Round Board
There is a variant of go played on a round board. Apparently it was introduced at a European Go Congress a few years ago: (dead link)
http://www.escape.de/users/shusaku/euro96/issue3/roundgo.htm
The board is an interesting spiral. A printable board can be found in PDF here:
http://www.youdzone.com/go.html
Some more mathematical information can be found here: (dead link)