How many combinations are possible in the game
Noughts and crosses)?
So for example a game which looked like: (with positions 1-9)
A1 -- B1 A2 -- B2 A3 -- --
 would be one combination
This information is taken from this website.
A naive estimate would be $9!=362\,880$, since there are $9$ possible first moves, $8$ for the second move, etc. This does not take into account games which finish in less than $9$ moves.
This gives a total of $255168$ possible games. This calculation doesn't take into account symmetry in the game.