I’m a big fan of the Asian board game Go. To me, it is a fabulous game, deeper than Chess, more of a metaphor for life, and reflective of the thoughtful, long-term perspectives you see in Asian cultures.
My interest was rekindled recently when I discovered the manga Hikaru no Go, after mentioning a desire to start a Go club at the local public school.
I prefer face-to-face games, but there are an amazing number of resources on the computer and the Internet. The current best resource seems to be http://senseis.xmp.net/?About. The site includes pages about how to get started, the basic rules, terminology (which is largely Japanese), books, and even game records and illustrations of basic positions.
If you already play the game, this site is pretty interesting: http://www.goproblems.com/
I love playing games of all kinds, but I don’t think I’ll ever tire of Go.