For example, Sovereignty Wars in EVE (taking territory from others) is a long, gruelling process that can go on for months. So the goons started launching their attacks at 3 or 4 AM on a monday, to force their adversaries to wake up and go into work with no sleep. They'd do this daily, for a month. In the end, rather than defeating their foe militarily, the opponent would get demoralized and give up, surrendering all of their territory rather than have EVE continue to affect their real lives.

Beyond that, though, they're simply an incredibly powerful faction. There's a resource called technetium that's needed in order to build any of the massive ships, so it's vital for any sizeable corp to have. The Goons grabbed a virtual monopoly on it, and formed OTEC which is a cartel whose goal is to fix the prices of technetium to make it so other groups could never match the goon's strength in massive ships, while growing ridiculously wealthy in the meantime.

Basically, the goons are just really shitty to play against. Couple that with the fact that they and reddit (who used to be the closest of allies) own about 2/3s of everything there is to own in the game, and many players really, really want them to go to war and kill each other off.

They're actually a major cultural force in EVE. ("Shoot blues" "Little bees") They're a bit like America in international relations, except there are fewer redeeming qualities.