Gonnect

From Wikipedia:

Gonnect is a strategy board game for two players invented by João Pedro Neto in 2000.

The game is played with standard go equipment (though 13x13 boards are often preferred to 19x19) and all the rules of Go apply, except that players can't pass and the pie rule is used to determine who goes first.

The goal of the game is to construct a group that connects any two opposite sides. A player can also win if his opponent has no legal moves (since suicides and passes are illegal).

Games between skilled players will end up temporarily deadlocked, since the square Go board allows a "four corners" configuration where neither side can strongly connect. However, since players can't pass, they eventually must start filling in the internal liberties of their groups. The player who has made the smallest amount of territory will presumably get killed first, so building more territory than your opponent is a secondary (but extremely common) means of forcing a connection and the win.

So, a gonnect game between similarly skilled opponents unfolds in two stages:

 The board-filling stage where opponents race to connect sides until the position is deadlocked.
 The eye-filling stage where opponents must fill in their own eye space or destroy their opponents. 

Although it shares many of the same tactics as go, some players feel that gonnect has a more interesting opening and endgame than Go. Most Go players, however, feel that the eye-filling stage of Gonnect is tedious, and that the game lacks the simple elegance of Go.