This game can be played on any size grid, below I show a game on an 8x8 grid. Graph paper works good. There are 2 players, one player plays the odd numbers and goes first the other plays the even numbers. When it's a players turn they have to play the next number to the left, right, above, or below the last number played on an unoccupied square, and when someone can't make a legal play the other person wins.
Here's an example game:
So you see the rules are so simple but the strategy and planning ahead can get pretty involved. I haven't named the game yet, I'd like to hear any suggestions.