Newly added: Check out this PBwiki that demonstrates all (okay, many!) of the different plug-ins that can add functionality to one of their wikis.
What – is a type of website that allows the visitors themselves to easily add, remove and otherwise edit and change some available content, sometimes without the need for registration. This ease of interaction and operation makes a wiki an effective tool for collaborative authoring. The term wiki can also refer to the collaborative software itself (wiki engine) that facilitates the operation of such a website, or to certain specific wiki sites, including the computer science site (an original wiki), WikiWikiWeb, and online encyclopedias such as Wikipedia (from Wikipedia)
Why – Because many heads are better than one, because collaborative writing is more exciting and rewarding, because you can encourage participation by group members, because you can have a historical record and electronic paper trail of the work you’ve done, and because you can easily share your results.
WetPaint has some of the best looking wikis available.
MediaWiki is open source and you can host your own site if desired. Used for Wikipedia. Wikia is one site where you can get a free, hosted MediaWiki site.
ZohoWiki was mentioned on the Web Office Suite page. Totally free.
Wikispaces is also very good and versatile. Basic service is free, but is ad-supported.