Years ago, I spent a lot of time working with an app called Groove. It was a little bit like Evernote in that it allowed users to sync between computers, but it was only available on the PC platform. It was also P2P... None of your Groove data was stored permanently on Groove's servers. Then Microsoft bought it, and last I heard, it had been rolled into Sharepoint Services.
Enough of the history lesson, though.
One of the shared work spaces I created in Groove was a collaborative writing space. The idea was that a group of people would work on the same story. The stories themselves were never going to be best sellers, but the practice was a great way to improve writing skills. Building off someone else's plot, adding your own voice, your own twists, then handing it off to yet another person to do the same forced you to think differently.
Evernote is a great way to continue this effort. Create a shared notebook with a group of creative friends. Each story gets its own note. Title the note with an idea, a starting point for that story. Start the story with a paragraph or two, or an entire chapter. Then let let someone else take the wheel. You could even tag the note with the genre or author names.
Keep in mind that Evernote doesn't lock a note when you start editing it... So you'll need some way of making sure two people aren't writing on the same story at the same time.
Give it a try. If there's anyone interested, I'd be happy to start up a shared notebook to get things started.