LineOfSightChess is like standard chess except that you can only see the opponent's pieces if you can attack them with one of your own.
This was the challenge at the XpCodeSprint held in PortlandOregon in April 2005.
Related versions of GameOfChess.
A chess variation I used (long ago) when teaching beginners who couldn't seem to anticipate what the opponent would do next was "ReverseChess?" where you played the pieces from the other side of the board, in other words, if the white pieces were set up on your side of the board, you played the black pieces.
After a few games done this way the ability to spot strategic and tactical weaknesses in your own position improved, often by quite a lot.
I recently envisioned an "atomic-age" variation of chess. Play by the normal rules, but whenever there is a capture, both pieces die and the square the capture was made on becomes "radioactive wasteland" (indicated by laying a checker or poker chip on that spot) -- nothing can land on that square, though pieces that move multiple squares in a single turn can pass over that square.