Listed below are some places where you can play Backgammon on the Internet. Some are simply playing against a computer, some you can register with and play against people from all over the world.

Motif - Motif is a Java applet that plays the game of backgammon. Good for beginners but it will still give an experienced player a good run for their money.

Gamesgrid.com - You are required to download their FREE software then sign up for a FREE account then you are ready to go against players from around the world.  By paying a small subscription fee you get access to more facilities.

Netgammon.com - Same as above down load their software and sign up and you are free to play.  They claim to have 20,000 players from 150 different countries so you can play 24 hours a day!

Yahoo Games - This will take you to their sign up page where you can sign in and then start playing.