Overleaf.com (previously WriteLaTeX) is a service that lets you edit & compile latex in the browser, with real-time edit merging.
It's comparable to ShareLaTeX.com. Notable differences (some unchecked since 2013):
ShareLaTeX is mostly open source. Easy to self-host on Sandstorm.
Overleaf doesn't require signup => Less friction when convincing collaborators to try it, just send them the URL and they can edit.
Overleaf's embedded preview uses images (fast but blurry), ShareLaTeX uses PDF.js. Both allow PDF download, of course.
ShareLaTeX has better history — shows diffs.
ShareLaTeX.com on paid plans has 2-way Dropbox sync allowing some offline/local editing (though only for one user; I tried it and wasn't impressed). WriteLaTeX only has 1-way backup to dropbox.
ShareLaTeX.com on paid plans has [sync with Github](https://www.sharelatex.com/blog/2015/02/10/sharelatex-github-sync.html; Overleaf supports direct Git access.
ShareLaTeX has embedded chat.
Overleaf seems to work better on Android & iOS. UPDATE: unclear, Android typing in Overleaf is also problematic as of 2016. I think the only way I ever got it to work acceptably on Android was with external keyboard?
Overleaf has forward/reverse search (SyncTeX), ShareLaTeX doesn't.