Ben Michell's Reversi is an iteration of the classic token-flipping board game. It provides a rotatable three-dimensional view of the board, with animated tokens, five different levels of AI, and hotseat PvP support. Legal moves, last moves, and suggested moves can all be displayed during play.
One of the great things about this adaptation of Reversi, which many digital board games get tragically wrong one way or the other, comes in the form of simple player selection. You can be black or white and face off against any of the AIs, or else face off against another human player sitting beside you. It's even possible to face off two AIs and observe their strategies.
Reversi's not a crazily complex game, but it's still mathematically unsolved, so you can have a little hope at least in taking on the strongest computer opponent. Regardless of ludic complexity, Ben Michell's version seems to include all the necessary elements, and does so in a very classy presentation.
Sam's Protip: Corners are key. Once you get a corner, there's no taking it from you, and you can use it as a hub for exploits along the also-potent edges of the board.