As old as the hills, this one — but then the best ones usually are! It is also known as 'Squares', 'My Box', 'Fields and Fences' and by various other names.
Two, three or four players can join in. Each chooses a different colour of crayon or felt-tip pen. First of all, a framework of dots is drawn in a square. For two players, seven by seven (49 dots) will probably be enough. For three or four players you will need more — possibly eight by eight (64 dots) or even ten by ten (100 dots).
The players now take it in turn to draw a line between two adjacent dots, anywhere on the square. This goes on until the square is crowded with lines. The object of the game is to complete a 'box' by drawing its fourth side.
The player who completes a box in this way shades it in with his own particular colour (if you haven't any colours, then use the players' initials). He is then allowed an extra turn. When all the boxes have been completed, the game is over. The player with most boxes to his credit is the winner.
The secret of the game is to avoid drawing a third line to any box, and so stop the player after you from completing it. However, you can't do this indefinitely.