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.latextemplates.com/ . Writelatex haven’t recently started the ‘Overleaf’ initiative, which seems to be an attempt to leapfrog traditional academic publishers, and do the whole write->review->publish within their system. Currently this seems to mean being able to publish directly to figshare, or submit to F1000.
I’ve used both with collaborators, and though the potential is great - we’ve always ended up forking the document & developing with a standard Latex install towards submission. You’d imagine this would be most useful on a laptop when travelling so you don’t need a full blown Latex install (>1GB), but these web apps get irritating on small screens & slow mobile processors.
If you have the collective technical skills, a (free) shared BitBucket private repo is the way to go.