Another popular use is to give group members a private forum on Moodle in which to communicate with each other. Even if you don't have students submitting their assignments in Moodle, giving groups a space of their own in which to communicate can help them collaborate more effectively.
See this tutorial on the Moodle Training Course for more information on how to create student groups on Moodle, and how to set up group assignments and private forums. See the video below for a brief overview: