Backgammon is yet another board game like chess but it's quite different. Like chess, backgammon has been subjected to extensive computer analysis and that has resulted in backgammon software that is capable of beating world-class human players.
One major difference is backgammon has more of an element of chance in it compared to chess so it's quite popular as a online betting game.
One such site that has backgammon as it's main game online is http://www.backgammonmasters.com. This site has a very international approach as they have included multilingual features into their website where their game lobby supports 14 different languages including French, German, Spanish, English, Portuguese, Danish, Hebrew, Arabic, Turkish, Greek, Chinese, Italian, Japanese, and now Bulgarian. Even their online support which currently supports English will be manned by multilingual operators in future.
Besides backgammon, the site also offers blackjack and poker software. Of course, this means the site is an online betting site so it's similar to casino/gambling site where real money is used. It's also natural for the site to support multiple currencies like USD, Euros, GBP and Canadian dollars.
So if you are into entering online backgammon tournaments with money at stake then take a look at backgammonmasters.com.