Tic-tac-toe is a simple and ancient game that you can easily play with the Green Box. Perhaps more an exercise than a game, as experienced players know that you can not really play to win, only to draw.
In Tic-tac-toe players take turns placing pieces of their color on a 3×3 board. You win if you are able to place three pieces in a row, and the game ends in a draw when the board is full and no player has been able to get three in a row.
Check out Wikipedia for more variations and detail, including history and the mathematical aspects of the game.
The game Three Men’s Morris is a variation where each player has only three pieces, so when all pieces are played the players start moving them to get them all in a row.
The game becomes more interesting if you expand the board and play for 4-in-a-row or more.
Also check out the Wikipedia page on M,n,k-games, the generic definition of this game with any size of board and any number in a row to win.