As a good first step, let's separate what a wiki is from how you can use it.
What is a wiki?
So. Wiki architecture presents the user with the skeleton of a website. There's no content, but there are plenty of opportunities to add content. There's no requirement that content is added by multiple users, or that the pages are open to editing, but both of those things are possible.Wiki is a piece of server software that allows users to freely create and edit Web page content using any Web browser. Wiki supports hyperlinks and has a simple text syntax for creating new pages and crosslinks between internal pages on the fly.
Wiki is unusual among group communication mechanisms in that it allows the organization of contributions to be edited in addition to the content itself.
Like many simple concepts, "open editing" has some profound and subtle effects on Wiki usage. Allowing everyday users to create and edit any page in a Web site is exciting in that it encourages democratic use of the Web and promotes content composition by nontechnical users.
How could you use a Wiki?
They can be used for all sorts of good stuff, but are most appropriate, I guess, for collaboration and the sharing of knowledge. Michelle Gorman of ComixLibrarian uses a wiki to advertise her workshops and to communicate their content.
Library Instruction Wiki is a wiki comprised of resources and teaching materials for librarians. This wiki includes a section on Library 2.0 in 15 minutes per day, which seems to be an equivalent program to 23 Things managed by Sam Wallin.
Library Success is a Wiki designed to collect best-practice information from library professionals and make that information available for sharing.
You no longer need to be able to code wiki pages in order to contribute. Most of these Wikis offer rich text editing. Vandalism and inaccuracies are also easily reversible. So... great for collaboration, (wikipedia) but collaboration not required.