Simply Gomoku

"Gomoku is an abstract strategy board game. Also called Gobang or Five in a Row, it is traditionally played with go pieces (black and white stones) on a go board (19x19 intersections); however, because once placed, pieces are not moved or removed from the board, gomoku may also be played as a paper and pencil game. This game is known in several countries under different names.

Black plays first, and players alternate in placing a stone of their color on an empty intersection. The winner is the first player to get an unbroken row of five stones horizontally, vertically, or diagonally."

Source: Wikipedia, "Gomoku", available under the CC-BY-SA License.