Are astronomy groups changing with the rise of the Internet?
I’m looking for examples of non-traditional Astronomy clubs, where there are no bylaws, no annual dues and no formal structure. Yet they have active members, regularly scheduled events and sell/trade equipment, just like traditional clubs.
Lots of yahoo groups are kind of like that. I am a member of some of them.

Lots of yahoo groups are kind of like that. I am a member of some of them.
References :
http://tech.groups.yahoo.com/group/digital_astro/
http://groups.yahoo.com/group/dynascope/
http://tech.groups.yahoo.com/group/QCUIAG/
http://tech.groups.yahoo.com/group/RoboScope/
Actually astronomers anticipated the internet by years with telex hot lines running from one observatory to another round the world. This system spread the news of supernova 1987A.
But a previous answer about some Yahoo groups is good. You might also find such groups attached to some popular astronomy websites, there is a fairly active forum attached to ‘Galaxy Zoo’.
References :