Well, that depends on how you wanna define "GG." I have 3 takes on it:
TAKE 1: "GG" signifying the game was well and truly an epic fight, and whether or not you lost, it was a good time nonetheless.
TAKE 2: "GG" signifying an event that, should it come to pass, pretty much means the other side pretty much has no choice but to wave the white flag of humility.
TAKE 3: "GG" signifying the common phrase used when the game's over.
For take 1, a lot of Castle Fight games I've played on Warcraft III: Frozen Throne have been like that. Castle Fight is a custom map in which you have a single, invincible worker to build unit-producing factories with. They can also build defenses or "Legendary" structures, as well, which use a piece of wood to construct (and a piece of wood costs 1500 gold to get 'em at your castle (the only way to get another piece), so they're not cheap). The goal is to simply overwhelm the other team and destroy their castle. There's a bunch of other details, but to get to the point, a game could last 5 minutes, or 2 hours, depending on how experienced you and your teammates are. And then there's some games that just reach a stalemate, and players can agree to call it a draw. The games I enjoy the most are the ones which both teams fight well, and whether or not I lose, it was still a great time.
For take 2, I have a technique that I like to use in Sins (should I ever get to said stage) with the TEC called the "Fan of Death." Basically, it involves putting a Novalith at every world I own in a star cluster (ideally, one that's well-protected), and then launching every single one at enemy planets. Since I hotkey my "Novalith Network," it allows me to quickly fire a volley of nuclear destruction at my hapless victims. Granted, since I've never played online, how well this would work is disputable, but it's fun to do, nonetheless.
Take 3 I don't think needs much more be said. =P