A strategy game (2 players, 20 minutes) played on a 4x4 board with 16 unique pieces. Each piece is either dark/light, short/tall, round/square, and flat/hole-on-top. Players place pieces until a row of four is created where all pieces in the row share at least one characteristic.
Perhaps the most interesting feature of Quarto is that every piece you place is selected by your opponent. You decide where to put it, and then select a piece for her to place. The winner is the player who places the piece completing a suitable row.