Confluence is a commercial wiki product used by many universities, open source software efforts, etc. It is a product of Atlassian, and provides rich and flexible editing capabilities and a plugin environment to extend the features of the wiki. There is an extensive range of plugins. Many organizations use it for documentation, group collaboration, project or course sites, knowledge management, internal web sites, etc. It supports a range of access control options for supporting anything from private to group to open-to-the-world access for viewing and editing. It also supports a range of export options that make it easy to get information out of the wiki in a form that can be easily re-purposed.
Non-profits and Open Source projects can use Confluence for free, and academic pricing is relatively inexpensive. See http://www.atlassian.com/software/confluence/pricing.jsp for more detailed information.