Tic-tac-toe is an old standby in the pen-and-paper game category -- make that a really, really old standby. It was actually played in ancient Egypt around 1300 B.C.E., and the Romans played a version as well. Instead of paper and pen, each player had three game pieces they would move around the game board for an attempt at 3 in a row.
Which, you might know, is the goal of tic-tac-toe (or noughts-and-crosses, as it's known in the UK). To play, draw a grid on your paper of two vertical lines dissecting two horizontal lines. Player one puts an X in a box; player two proceeds to put Os. The point of the game is to try to get three of your marks in a row or to block your opponent from doing so. But beware, the clash of two experienced tic-tac-toe players will often result in a stalemate.
Technology is such that you can now play the game online for free or print off grids to save your wrist the trouble of making them yourself.