As an undergraduate art major, I used to enjoy writing collaboratively on addventure. It was an early site for authoring hypertext (click-through) fiction where users could add to a story from the character decisions that were left open at the end of a paragraph/chapter. Pretty much like writing a Choose Your Own Adventure book collaboratively.
A few years ago, an online acquaintance of mine named Joakim Johansson started a website called Story Wars. In SW, users are able to author the first chapter of a story which then is open for drafts on the next chapter. Anyone can submit a draft for the next chapter. Once at least two new drafts have been submitted, they are revealed anonymously for the community to vote on. The chapter with the most votes wins and goes on to be the fixed next chapter of the story. And so on.
I also recently found Storium. Storium blends elements of collaborative writing with tabletop roleplaying games, using a card system to develop characters and narrative. Pretty fun stuff.