I personally use threaded discussions related to my hobby (scrapbooking) almost every day if not several times a day (twopeasinabucket.com). I had never really thought about using them as a part of my teaching.
From what we read and the discussions we had yesterday, I can see how having students do threaded discussions could be beneficial. When we did it in class, we were able to all "talk" at the same time and share our ideas, so even those who did not want to speak up in class were able to share ideas for all to benefit from. If I use this in my classroom (or when I do), students would be able to add to the "conversation" at any time. After a class or discussion, I have often thought of a new idea or another comment, I could share those further ideas if we were using a threaded discussion. These discussions also provide a written record of what is being shared. I may not have heard someone's idea if we were having a large oral discussion, but using this type of discussion, I can go and read what that person shared.