I’m not into collaborative writing (because I’m a control freak when I get really into a story), but if you’re into that kind of thing, StoryJoin might be a good website for you.
Read finished stories, start your own story, or contribute to an unfinished story – it’s up to you. You can write as much as you want on any particular story, but be open to the many ways in which a story can go!
The website seems to be fairly new and simple; there aren’t many features and only 8 categories of writing you can submit work under. I’m not sure if fanfiction is allowed or not.
Either way, collaborative writing is a good exercise to hone your skills, meet other writers, and perhaps get some good ideas. Check it out! 🙂