I would suggest the chinese version of chess, xiangqi above all. Heres a website to play it online: http://www.clubxiangqi.com/
Also check out japans version of chess, shogi. Never really got into that (lack of opponents)
Personally I would suggest sticking to chess. It never becomes dull, you can spend your entire life (and indeed, many have) and still not master the game.
I absolutely love every aspect of chess but lately I have been looking for a game thats LIKE chess and has every strategic aspect but a new flare. Perferably free as I don't have much money. So far I have found Zatikon which is a really good one but I was wondering if anyone else knew of any besides Zatikon... Thanks!