If you enjoy collaborative writing, Protagonize may be the site for you. It’s been around since December 2007 and it caters to both experienced and new writers. Of course, it’s free.
You sign up and either start a new story or poem or add to an existing one. However, you should follow the original author’s set of guidelines for the story, so that it stays consistent as it’s being written. Your added sections to a story don’t have to be long; 250-300 words is recommended.
Like any other writing site, you can comment on and rate works. You can choose to be notified when a work you enjoy is updated and you can add your own bookmarks so you know where you’ve left off.
So check it out if you’re into collaboration! And even if you’re not, writing a piece onto an existing story might be a good writing exercise. 🙂