TeX implementations in the Cloud

The more mature products (2014)

• ShareLaTeX
  XeLaTeX and pdfLaTeX, biber and biblatex.
  Based on the most recent TeXLive.
  • Open-source version of ShareLaTeX for self-installation.
• Overleaf (formerly WriteLaTeX)
  XeLaTeX supported since March 2014.
  Based on the most recent TeXlive.

Both the above have collaborative-editing features.  Both have free access for limited projects, but require subscription for larger projects or collaborative teams.

Others of varying levels of activity (2014)

• FlyLaTeX (self-hosting; free and open-source)
• TeXTouch (iTunes, iPhone editor, can compile when online)
• Verbosus (with Android and iOS apps)
• Blue Publications
• LaTeXLab - requires your Google login details :-( 
• Pine from Sayahna.orgIn alpha test (a document processing system in the cloud that makes use of MediaWiki and its resources)
• CloudTeX from Sayahna.org
  XeLaTeX and LuaTeX supported.   Working prototype available to testers. 
• A different CloudTeX Seems to have gone quiet as of 2013.
• SpanDex
  XeLaTeX and LuaTeX available, but limited Unicode fonts. Closed.
• ScribTeX  (phased out as of Feb 2013, in favour of ShareLaTeX, but still exists)
• MonkeyTeX (4/2014)