Morris is an implementation of Nine Men's Morris that also supports several rule-variants and different board layouts (including Morabaraba). You can play against the computer, or play against another human opponent. The computer opponent learns from previous games and tries not to make the same mistake twice. This ensures continuous variation in game play, should you manage to beat the program. Furthermore, the program can give move hints and provides unlimited undo/redo.
Lux is a game of strategy and domination inspired by the board game Risk. Control your armies to conquer and hold strategic countries on the map. The object of the game is to take over the entire world. In addition to the classic Risk map, Lux has a variety of different maps available and features a map editor to create new maps. The map files are in a documented XML format. Lux comes with computer AI players ranging from easy to hard. There is also an SDK for creating robots and an Internet game tracker.
Oligopoly is a Monopoly-like game as a Java applet, directly playable from the Internet. It's written in Java and the object design is very true to the game. It should be easy to modify. It comes with nice graphics and is quite fun, although it lacks many features of the original game. It is currently only in German.