People mention Google Docs a lot in this thread.
There seem to be a server version of LibreOffice, called confusingly LibreOffice Online and Collabora Office (?) somewhat interchangeably; Collabora is the #1 contributor to LibreOffice.
I cannot find a free online demo of that though, so I don't know how good it actually is.
edit: there is also some confusing thing about maximum number of users, and if you want to remove it, you need to rename the server because of trademark? I don't know. Seems confusing