National Space Society
The National Space Society, formed in 1987 from the merger of the National Space Institute and the L5 Society, is a space advocacy group rather than the kind of society you can actually live in. Their mission statement, however, is to create not just a society, but a whole "spacefaring civilization" that will allow people to live and work in space. In service of this ambitious goal, they publish Ad Astra magazine and hold the annual International Space Development Conference, and also help sponsor the SEDS SpaceVision conference. They also recently announced a project to promote Space-Based Solar Power, in collaboration with a former president of India. In fact, despite its name, the NSS has three chapters in India, as well as chapters in six other nations beyond its native United States (plus one in the semi-foreign land of Puerto Rico). The unambiguously "national" part of the organization includes 56 chapters in 27 states.