Daoqi
Derived from Go.
Co-invented by Qibin Xu and Guoliang Cao.
The Daoqi board is continuous, in that the last line wraps around to the first line, for both horizontal and vertical lines. That is, there are no sides or corners.
For more information, visit daoqigame.com
See also Unusual Gobans (toroidal board)
Bildstein: We should have an ongoing game. 19x19, and at each move we display the board from a couple of different perspectives, probably 4.
unkx80: See http://www.daoqigame.com/en/daoqi/articles/introduction.htm for how the authors represent the game.