Group projects and group discussions are another way to assess your students. One benefit of the online world is that you can keep tabs on how much work each student is doing. For example, as part of group work, require students to have an online chat about their work. Students must then submit a transcript (cut and paste) of their conversation, which will count toward their grade.
Students have a variety of ways to network with one another, so have them make use of chat rooms, instant messaging, email, and discussion boards and turn them into online assessments.
Provide structure to your discussions so that students know they are expected (and graded) on making a certain number of posts per week. You can require these posts to be replies to other students, commentary on reading or video, or general thoughts about a subject.
Whatever assessment methods you choose, be clear about your expectations, timeline and grading policies. Rubrics are a wonderful way to convey your expectations. I have used RubiStar to create many rubrics and it is a fabulous tool.