Backgammon Snowie
Demo. Single or Multi Player. Great backgammon game, easy instructions and 8 different levels that you can choose to play against. Has a great help section. Won't take long to play against the computer. Even will auto finish your game.

JellyFish Backgammon for Windows
Freeware. A neural net based backgammon program that plays at a very high level. It matches the best humans in the world, and on level 5 a top human will hardly win more than 55% of the time. Also, its use of the doubling cube is outstanding.

David's Backgammon
Demo. Single or Multi Player. David's Backgammon has 5 skill levels. Features include ability to play against the computer or a friend, advice on moves, a doubling cube, online help, multiple board sizes, tournament play, and statistics tracking.