Here's a really cool one: Play65 lets you play backgammon online against real people.
And if you want, you can deposit money and play real people for real money (or just play for fun money if you prefer).
I even managed to get some coupons out of them so if you do decide to play for real money you can get more credit than you deposited.
Use any one of these bonus codes when you sign up:
Get $5 for depositing $25: OGTB25
Get $10 for depositing $50: OGTB50
Get $15 for depositing $100: OGTB100
Enter one of these bonus codes during the sign up procedure in the "Sign up" bonus code field (the bonus is redeemable when you first deposit).
Play the game