One who dubs himself the Pathology Guy has an amazing page with scores of chess variants, each with a computer opponent to try it. It would take days to try all the variants, but here’s a few I found the most interesting out of the small percentage I experimented with:
Dark Chess: You can only see the squares your pieces are allowed to move to. Knights can be really annoying. In many ways the darkness is an equalizer, certainly more than making up for the weakness of the Java chess engine. Dark Chess II prevents you from moving into check, a luxury not afforded by the first one!
Soccer Chess: Use pieces to kick a ball into a goal. There’s no pawns and no capturing.
Strong Pawn Chess: Instead of their normal movements, pawns act as a weaker version of the pieces behind them in the initial setup. For example, Bishop Pawns move one square diagonally. The center Pawns are very strong and move like Kings–don’t underestimate them!
Unfortunately, the Strip Chess variants are not working at this time.