Online
Play backgammon for no charge on a free website. Try Play65, Nabisco World or the Great Day Games website. These are some of the largest backgammon servers on the Internet. These sites allow to you play for free in one-on-one games or in online tournaments that they sponsor. While you are never charged to play a game, you do have to option of becoming a premium member on some websites and playing for money.
Friends and Family
Ask for a backgammon board for Christmas or your birthday, and you'll never have to pay to play. Invite your friends and family to a friendly one-on-one game, or set up your own free tournament. Not only will you be spreading the love of backgammon, you'll be creating new opponents to play with. Try serving some snacks, and you're sure to find plenty of friends who would like to play you in backgammon.
Electronic Systems
Download a backgammon game onto your phone or gaming system. You'll have to own the device first, and possibly pay for the download, but after that, every game is free. There are even backgammon apps that are free to download on both the Android and iPhone. Some are so advanced that you can even play against live opponents. A backgammon app will give new life for your ten-minute wait at the bus stop or doctor's office by providing endless entertainment.
Move Over, Bingo!
If you can't find any local free tournaments in your area, make one. Check out your local American Legions, Moose Lodge or church to see if they would be interested in hosting a friendly game for the community. Go to the American Legions website to find the local chapter in your area. Most already host bingo or pinochle games and might be willing to squeeze in backgammon if enough people show great interest. While this may take some convincing on your part, it would give you and your friends a free venue to play your favorite game and meet other enthusiasts.