First is an excellent group writing activity that is especially good for freshmen at the beginning of the year, and as a bonus, it integrates technology. This blog explains the professor's project for college freshmen, but it could be easily adapted for a younger crowd.
Faculty Focus Real-World Writing Project
Next is a video of group writing in action from a high school English teacher. It shows her whole process, which is easily adaptable for whatever topic you are addressing, and gives tips to make the whole thing effective. It's interesting that although it is a writing project, the teacher says that the discussion in the most important aspect of the activity.
Teaching Channel - High School Writing Lesson
Last is a fun collaborative poetry project from the Literary Maven. I'm not sure how I will work this into my curriculum yet, but I'll figure something out because it looks like a lot of fun.
The Literary Maven - Collaborative Poetry Writing
The group writing activity I use most often in my class is one on figurative language. I go over the definitions of six or seven types of figurative language and then show a piece of art. Groups have to come up with an overall thesis, then write one of each type of figurative language relating to the thesis about the artwork. It's easy enough to set this up yourself, but if you want my teaching packet, you can see it here: