In Hex, two players take turns putting playing pieces on hexagon-shaped tiles on a hexagonal board (which looks similar to Chinese Checkers). The winner is the first player to create a "bridge" - an uninterrupted chain of pieces that connect two opposite edges of his/her color. The game is a lot of fun, especially against a competent opponent or computer AI, because it's impossible for a draw to occur. Either player eventually wins at the end, when all empty tiles are filled. Effective defense is often the best strategy to win the game, because if you can successfully prevent the opponent from creating the bridge, chances are you will yourself form the bridge.
Hexy's AI certainly meets the challenge, as it features arguably the strongest Hex player today. You can change board sizes depending on how much playing time you want. If you enjoy abstract strategy games, Hexy is an outstanding freeware gem that is great for those 10-15 minute coffee breaks. Highly recommended!