I have taken part in all sorts of writing that could be described as collaborative. I was in an amdram group and we wanted to put on a murder mystery. All those who wanted to take part in the mm wrote out a brief background history of their character. I took the 'characters' away with me and used them to write the plot of the play that was eventually put on. During the first rehearsals there was quite a bit of improvisation and this was eventually scripted.
The second time was on a message board where a group of us wrote a story chapter by chapter. We had a running order and a time limit. Basically a list of names and you had to post your chapter within a specific time frame. It was great fun as we never knew where the story was going or how it would end. The group did quite a few collaborations, some where plotted and some were not. We also did collaborative stories as birthday presents for each other - they were done in secret with one of the group overseeing it. Some of the group were artists and/or photographers so there were pics as well.
Last and most recent was writing Shakespeare Sandwich for the Mere Players, the local amdram group. It was written by myself and the director/producer. It really was great fun and I enjoyed it, although we did have to meet up to discuss where we were going with it.
I have enjoyed all off the collaborative writing I have done and, mostly, found it stimulating to bounce ideas about. I also found that I could not be precious about my work and had to go with the group feeling even if it went against mine.
There were three things that were annoying and frustrating. People who said they would take part, insisted that their take on the plot/story line was the correct one and then said they did not have the time to write their chapter. Badly written and careless work, not spell checked and just thrown at the rest of the group with a cyber shrug of the shoulders! One chapter, nearly three thousand words was written entirely in lower case and with no punctuation. Lastly there were some group members who did not bother to read at least the chapter before the one you had to write so the chapter submitted made no sense and did not fit in. Sometimes the chapters would have totally different characters and locations.