I have a confession to make - I am a bit of a sucker for exotic stuff. Perhaps that's why I have a weakness for chess variants, a thing which Proper Good Chess Players (tm) should scorn at.
I try them not because I am tired of chess, (how dare me!) but just because variety is the spice of life - and I sometimes do feel the desire to play something new but still chesslike.
I play the predecessor of modern chess, the Shatranj (http://en.wikipedia.org/wiki/Shatranj), when I don't want to engulf myself in tactical complications. Shatranj is a quite slow game - and through that's the reason why it was abandoned in the favour of modern chess, that change of pace feels rephreshing sometimes. (Althrough the Alfil is such an awkard piece...)
Chinese Xiangqi and Japanese Shogi are very nice too, and can be even more tactical then Chess.
From the modern inventions, I am intrigued by Chess With Different Armies. (http://www.chessvariants.com/unequal.dir/cwda.html)
Of course, the main root of the Chess Variant tree - Chess themselves - is healthy, and doesn't need any artifical changes. Still, that doesn't mean that the existence of al other roots should be forbidden.