Blox

From the game's website: Blox is a strategy game played with building blocks such as those manufactured by Lego(TM) and Tyco(TM). Players compete to construct a 3D chain of blocks on a base plate. Very simple rules lead to a surprisingly complex game. The goal of the game is to be the first player to build a chain of their own blocks that connects all four edges of the board. All players could complete their own chains, so the first one to do so wins.