From Rethinking Synagogues, by Larry Hoffman:

Academic communities: Scholarly communities where members demonstrate their right to belong by reading or publishing professional papers, and try their best to prove each other wrong.

Therapeutic communities: Communities for people with common problems, where members offer mutual support and distinctly try not to prove each other wrong.

Market communities: Communities that exist because they promise concrete benefits, not because they are so central to people's lives that their members cannot imagine belonging anywhere else.

Limited liability communities: A particular class of market community, offering specialized services for a fee, and the kind of community that most of us belong to today.

Sacred communities (Kehillah Kedoshah): Communities whose worth is measured in sacred acts and relationships that connect us to one another and to God.