Anna- The regional museums I work with were begun for variety of reasons- usually nostalgia for a romanticised past, celebrating a community or an event anniversary. Most teeter on closure because there was no over the horizon planning for sustainability.
I think Jane is right. The museum volunteers and staff that embrace digitisation and social media might be the ones who survive and even thrive. This would include a conceptual shift of what a 'museum' is. Lots of community museums might actually reach a larger and wider audience if they digitised their collection and ran their museum as a virtual one. Then they wouldn't have to worry about the logistics of running a 'bricks and mortar' museum with its ongoing running costs and staffing headaches in keeping it 'open' to the public who usually don't visit in great numbers anyway. Then they could focus their resources on strategic planning, collections management, research, online interpretation and audience development. Furthering regional networks such as C.A.N. and Museums Australia would give them more clout too. But then what would I know I am just a hologram...
Many local museums I'm familiar with were historical societies first. A museum often followed as a natural progression. Jane and Stephen seem to have covered well the reasons on why they were formed.
I think they're highly relevant. No two communities have a common history. They all have their own past, their own stories, disasters and victories. Even for the historical events that touched every community - there is a different impact, slant and voice in each locality.
Furthermore, if local museums were relevant 30 years ago then I'd argue they're even more relevant now. They now have another 30 years of history, stories, experiences and objects to share! The story goes on.
The internet definitely offers new opportunities. It allows museums to put themselves out there so people can discover their existence. It also provides a form of publishing that has the potential to reach an extreme number of people.