Windows
3DFiBs Backgammon
Some of the features you will enjoy with 3DFiBs..

• Smooth animated checkers on a nice board.
  
• Tool bar buttons for convenient access to commands.
  
• Real time player list updates including your own "Friends" list.
  
• A basic "save game" as JF.mat feature to play-back/analyze offline.
  
• Play off-line against GnuBG backgammon engine with hints.
  And many more features to enjoy the wonderful game of backgammon

Gnu Backgammon for Windows
One of the strongest programs on this list. It has nice graphics, comes with a tutor to point out your errors. Gnu BG can analyze games and matches you play online or play against the computer.

Jellyfish
The first commercial neural-net backgammon player. Expert level player (one of the strongest games on this list), and an excellent opponent to practice against. Play single games or matches. Save games and replay them later.

Pro Backgammon
Five match-play options. Four levels of computer play. Play with others over a LAN or on the Internet. Free Lobby to find others to play with all over the world. Thirty minutes of music.

Palm OS
Backgammon 3.1b
A well featured, lightweight and free Backgammon game. Play against your Palm or another human player. Learn basic strategy by having your Palm playing against itself.

PocketGammon
Classical backgammon for Palm Pilot.

Mac
Backgammon 2k
Save and reload games. Use doubling cube. Choice of computer-rolled dice or manual entry. You can take notes. Choose from several styles of player. Take back and replay moves. Get advice on how to move.

Gnu Backgammon for MacOS X
One of the strongest programs on this list. It has nice graphics, comes with a tutor to point out your errors. Gnu BG can analyze games and matches you play online or play against the computer.