Tic Tac Toe - Verifying a player won
One thing that comes to mind is probability.

In all winning cases of tic-tac-toe, the middle spot of the involved row/column/diagonal is always occupied.  Therefore, I would look to spread my chances and test from the most frequently occupied space(s) in the middle and keep trying to test one adjacent space outward at a time in an evenly spread fashion.

The benefit of this really comes into focus when you think about the fact that the whole check is really done in one pass in a spiral kind of manner.  Having the check in one pass means that as soon as you run into a space that eliminates the possibility of a win being present, you stop checking it.  Therefore, the spiral will go faster and faster until a win is found or until the whole check is completed.  Pretty cool to think about.

I may code this...but for now that's just an idea of one interesting approach you can take :)