Alternate Board Shapes

So, something that I was thinking about was turning TF2 (An FPS) into a form of chess, which took me to the more general idea "Has anyone ever used alternate board shapes for chess?" 
Most of the time, Chess is played on a square board with 64 individual squares. Even with the variants offered on Chess.com, the most "out there" the shape of the board gets is the overlapping rectangles of 4-Player chess. Are there any particular shapes that could be used effectively as an alternate chess board? Has anyone attempted this before? Would there be a considerable amount of compromises needed to the original ruleset of chess?

The only idea I have, myself, for an alternate chess board is a doughnut shaped board, that being a circle with an interior diameter missing. For this board, there would definitely need to be compromises made for pawn placement, as, with the blocking of the center, it would be very difficult to advance pawns forward by just taking the opponents pieces/pawns for lateral movement. If anyone else has ideas/precedent for alternate board shapes, please do share!