Picking up from Jason's recent wiki post, I meant to offer a few particulars about how and why I've been using wikis in comp class. The ideas of social construction and knowledge-building by consensus that stem from how wikipedia functions need not apply to the wiki as used in the classroom. (I'll offer that as hypothesis, anyway.) The analogy I'd suggest is the electronic bulletin board.
I first used wikis a couple semesters ago as the space for research groups (four or five students per group) to collect up entries for an annotated bib assignment. Students selected first and second choices from a list we'd brainstormed together; I made assignments, trying to even out numbers and skill levels in each group. Students then had to decide how to divide up the workload of locating both Internet and database articles, providing a very brief (couple sentence) summary, and evaluating with specific evidence of amount of usable material, authority and objectivity of author (the usual criteria I write on the board sixteen times a semester). Using the wiki allowed students to post hyperlinks to articles, so that others in the group could check out summary and evaluation. I posted comments and questions on esp. strong or weak entries (using some distinctive color--I had asked students as well to type their name in a unique color so that they, and I, could tell who had written what). Of course, I could have done a similar thing in google docs, but the public nature of the wiki allowed students to look as well at the work of other groups, and a later writing assignment allowed students to draw sources from either their own research wiki or another group's.
A second way I've used the wikis just this semester involves my standard beginning-of-the-semester assignment the classmate snapshot. (Briefly, students interview each other in order to write a sharply detailed--in theory--paragraph that provides a snapshot of their subject's life.) In the past, using course management software, I have asked students to post these on the discussion board provided, but the wiki is a much cleaner interface, with snapshots all appearing on the same page (none of that cumbersome clicking in and out of posts). And because I'm using course blogs, it was an easy matter give students hyperlinks to the wikis I had set up (one for each of my classes).
In short, I've been using wikis not for their wikipedia-like possibilities for collaborative work (several students producing one joint project, like many sculptors moving over a large piece of sculpture), but rather for their convenience (in terms of being able to hyperlink), their simplicity of navigation, and their public nature (for helping to build community).
Your question(s), then: With what types of assignments have you used wikis? Why wikis, rather than some other format? If you haven't used wikis, why not?