This is another weird one as it doesn’t appear specific to my own gaming group, but any gaming group. I could google to find some neat examples, but I’ll focus on my own experiences.
Most of my gaming groups have been small gatherings of friends, getting together to hang out and play games. So, banding together together to do something for the community is kind of like asking what a group of poker players did for their community. Probably not much.
I think that what game groups have done though, particularly ones that put on “open to the public” games, is offer people who are otherwise isolated and don’t have a game group an opportunity to play and get to know other gamers in their community. As such, those open games are an important service that GMs can provide to their local community.