If you have a G1 Android phone, you can try out two games that I developed. They are available for free at the Android Market.
Chess for Android is a simple standalone chess application, consisting of a chess engine (derived from BikJump) together with a GUI (thanks to Joseph Wain for designing the chess graphics). The application accepts moves through the keyboard or touch screen. Once a source square has been determined, all valid destination squares are shown in green. The engine plays at various levels (including random or against itself).
Reversi for Android supports keyboard and touchscreen input, and displays all valid moves through labeled "ghost" stones. This engine also plays at various levels (including random).