Tic-Tac-Toe, also called Noughts and Crosses, is a classic game between two players, "0" and "X", that alternate in marking the spaces in a 3x3 board, trying to put three of their own marks in a horizontal, vertical or diagonal row.
For instance, in the following game, "X" has won:
O|O|X -+-+- X|X|X -+-+- O|X|O
In a normal 3x3 tic-tac-toe game, both players have a strategy to draw the game. In fact, any move by the first player leads to a draw with best play.
Statistically the best opening move is in one of the corners, after this move has been made if the opponent takes any square other than the centre one, then the first player can play in such a way that a win is certain.
There are some variations: 4x4, NxN, and 3D tic-tac-toe.
Perfect play is known to be possible 3D tic-tac-toe when played on a 3x3x3 and 4x4x4 board so that the player who goes first can always force a win.
On a 3x3x3 board it is relatively trivial to win, the first move should be in the centre, the third move should form a link of two in such a way that a blocking move will not allow the opponent to create two in a row, now a forking move will be possible such that on the players next move their will be two place they can go to win. The opponent will be able to block only one of these and thus the first player can take the other and win the game.
The 4x4x4 board game was solved recently by Victor Allis.