the number of possible games of Go FAR exceeds that of the number of atoms in the universe.
on a 19x19 board, there are approximately ~0.011957528698 * 3^361 ~ 2.081681994 * 10^170 legal positions in Go (
http://homepages.cwi.nl/~tromp/go/legal.html).
With 361 possible moves, you have 1.7 * 10^766 possible games, and, allowing captures and unlimited stones, you have 2.1 x 10^2807 possibilities.
Let's put it this way...
This is a quote from
http://senseis.xmp.net/?PossibleNumberOfGoGames
"The harder question is trying to figure out how many possible games there could be that actually make sense as games which might happen between two rational players ...
Let's lowball and say the average game is 150 moves, and that on average a player is only seriously considering about ten possible choices per move, so 10^150, and dividing by eight for symmetry still gives 1.25* 10^149. With only looking at merely five choices per move, that still gives a result of 8.75 * 10^103, or 23 orders of magnitude greater than the atoms in the universe! I wouldn't count on repeating a game anytime soon..."
From personal experience, I can tell you that 150 moves is ridiculously short for a Go game on a 19x19 board, and to say that a player is only going to consider, on average, about 5, or even 10 plays per move, is a very, very, very large simplification and reduction of the complexity of Go. Even in this very simple, reduced case, the number of possible go games is more than a googol.