Quick Backgammon - Formerly Geert's Backgammon
Freeware. Single Player. Quick Backgammon lets you play backgammon against the computer, offering several levels of play and interesting statistics. Other features include adjustable color schemes and customizable skill levels.

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.

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.