You know, there are other interesting "chess" variants that are not even chess at all, despite the superficial resemblance. They might be worth checking out.

Arimaa - Due to Kasparov's defeat at the hands of Deep Blue, game inventor Omar Syed decided to invent a game that can be played with a regular chess set, can be easily learned and played by humans, but cannot be played well by computers (at least at the present). The wiki article is really worth the read, as is this link as to why there is such a difficulty in creating a competent computer player.

Ultima - Like Arimaa (though much older in invention), Ultima a.k.a. Baroque chess can be played with a standard chess board and pieces, but is a very different game. In chess, pieces capture in the same manner, but their moves are different. In Ultima, pieces move the same way (for the most part), but their means of capturing is different.