Sharelatex is now opensource: https://www.sharelatex.com/blog/2014/02/21/sharelatex-is-now-open-source.html; discussion on HN: https://news.ycombinator.com/item?id=7276263. They also now offer a ‘personal’ account which allows for unlimited projects + one collaborator.
The other big player in this area of collaborative online Latex document editing is https://www.writelatex.com/. I’ve generally found their web app to be a little bit heavier on the computer (particularly my poor old Thinkpad X60s), but more polished. You can directly open a Writelatex document from templates at http://www.