Use a wiki for an "ice-breaker." Have each student interview another student, write a brief biography, then post that to a class bio wiki.
Have students create a class expanded bibliography or resource wiki. Each student posts one or more articles or resources, then writes a brief description or informative summary of that item. They can be organized and exported as a collection for students to take with them at the end of the course.
Annotation assignments: have students annotate a literary work, article, or other piece that you post.
Topic or assignment claim list: post a list of topics to a wiki page and have students sign up for their chosen topic by simply adding their names next to it.
Have students build a course notebook. Assign one or two students to take notes during each class, then post those notes to a wiki.
Create a class glossary. Have students choose the terms to be defined or you provide them ahead of time.
Create a wiki space for each student to write their individual research paper or major project. They can use it for the drafts and for the final product.
Create a wiki that will become a website. Choose a major topic and have each student contribute a section.
If you have students create Powerpoint presentations, consider having them post these to a central course wiki page.
Group report: have students write a collaborative report where each student contributes one section. They can also devote one page of the wiki to assigning roles, deciding and documenting who will do what, or tracking progress. For example, students may be resources collectors, writers, editors, organizers, or all of the above.
Have students create or augment a Knowledge Base, Study Guide, or Help Guide for the class. Each student can be assigned or choose a topic for which they will become the "expert." This can be recreated each semester or can be carried from semester to semester for each class to contribute to.
To have a successful wiki experience:
Make instructions explicit and provide clear expectations
Build in time for practice
Publish due dates for multi-phase projects
Start with a simple wiki assignment before attempting a large, collaborative project
Visit Wikipatterns.com for information on what to expect from your students as they begin to write collaborative wikis.