Backgammon is one of the most popular board games around. There are already plenty of decent backgammon apps that can give you a good game. Prefer to play on a real board against the computer? The Saitek Electronic Champion Backgammon has you covered. It is powered by a 16k AI from the 1989 computer Olympiad.
The computer can not only suggest moves but play against itself. You get auto and manual dice options. According to the manufacturer, this board knows the rules for Backgammon, Jacquet, Tric Trac, Moultezim and Plakoto.