For instance, the following game was won by the first player, "X":
 X O X O X O X O X O X O X ++ ++ ++ ++ ++ ++ ++       O O OO OO ++ ++ ++ ++ ++ ++ ++     X  X  X X X X XXX
In a normal 3x3 tictactoe 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, as shown in the above game.
In 3D tictactoe, when played on a 3x3x3 and 4x4x4 board, the first player can 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 there will be two places 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 same applies for any number of dimensions (i.e 3x3x3x3, 3x3x3x3x3, etc).
The 4x4x4 board game has been solved. Victor Allis[?] showed in 1994 that there are 76 different possible winning lines.
An interesting variant is inverse tictactoe, in which each player tries to force the other to get N in a row.
Another interesting variant is 9 board tictactoe. The nine boards are themselves arranged like a tictactoe board. The first player's move may go on any board; all moves afterwards are placed in the empty spaces on the board corresponding to the square of the previous move(that is, if a move were in the upperleft square of a board, the next move would take place on the upperleft board)  should all nine squares get taken on a board and the last square taken points to the full board(unlikely), the next move may go on any board. Victory is attained by winning 3 in a row on any board. This makes the game considerably longer and more involved, with a definite beginning, middle and endgame.
An interesting extension of this idea is the commercial game Quarto (http://ssel.vub.ac.be/Members/LucGoossens/quarto/quartotext.htm) which is played on a 4x4 board. There are 16 pieces each with four aspects:
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