Are there any places or ways a group (general public or individually invited) of people can individually contribute to a communally developed story?
For example, a website or collaboration tool (besides Word files emailed back and forth).
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You could start your own wiki - if you need hosting, there are plenty of resources available for cheap/free wiki hosting (PBWorks comes to mind.); you could use any of the browser-based shared document editing tools (Google Docs, Zimbra, Zoho); collaborative editing software (see this Wikipedia article for some examples).
I'm currently collaborating on a screenplay with a writer in another country. We're doing the research, outline and treatment in Google Drive.
It's easy, and you don't have to pass documents back and forth:
There's a Yahoo group, now apparently inactive, at http://groups.yahoo.com/group/rr-storybook/ that was set up for round robin stories. The last hint of activity seems to be around 2006.
If nothing else, you can look at what we wrote, and how it seemed to work. The files seem to be outside the members-only area. I don't know if there's any group administrator who could get it going again.
Since it hasn't been mentioned as an answer to this relatively old question: Pan Historia is a casual and fun place to collaborate on writing. The community is quite supportive, although the turnover seems high.
There is a Facebook group called Indie Writers Unite which has an ongoing thread that is attempting to do this. So far I believe they have about seven chapters completed in a fantasy novel. One person will write a chapter and then it gets handed off to the next person to write the next chapter. Last I saw they were looking for people to help contribute to this.
I am the lead programmer for a project called Fablelane where people contribute small segments to a story. One segment can have multiple outcomes, so a tree of choices is formed.
People so far think it's quite fun. You may enjoy it too!