The following 3 websites are recommended:
This is regarded by some as the best backgammon software program in the world:
The portable version, XG Mobile, can be found under:
One other recommended site for portable devices is:
Most other backgammon playing sites, by comparison, are feeble.
Playing for money
Many online backgammon websites are not looked upon as safe, but there are some, like Money Gaming and DailyGammon, that are reputable.
Generally, it is best to tread very carefully, using only websites recommended by backgammon players known to you. Also, never play for large sums of money because you could be playing against several players or even against a player using a software system like XG.