Neither Zoho nor Zimbra have open source self-hostable office applications.
But I've been looking at this again, and have discovered some very promising candidates for online, web based, self-hosted, open source "office" applications.
For online Word Processing, either EtherPad Lite or FengOffice (or EyeOS) will probably do well. The former includes real time collaboration.
Online Spreadsheets were MUCH harder to find. GelSheet is rather slick, and has FengOffice/OpenGoo integration, but isn't officially sanctioned yet. WikiCalc/SocialCalc is even slicker, but most of its iterations and forks have only minimal import/export capability. So the big winner seems to be "Sheetster CE" (technology also known by OpenXLS, Extentech, and ExtenXLS), which is rather full featured, if a little slow due to the Java.
I think both the multiuser EtherCalc (Audrey T's SocialCalc fork) and Sheetster allow real time collaboration.
So EtherPad + Sheetster makes for the beginnings of a pretty compelling online open source office suite.
(Or using FengOffice or EyeOS as a base to cover Documents and Presentations and adding in Sheetster or SocialCalc for spreadsheets.)
I'm writing about it here because, for some crazy reason, this essential information is really nowhere to be found on the Internet!
As to LibreOffice Online, it's still "coming soon". It could be a game changer though.
> When will LibreOffice Online or the mobile app be ready for general use?
> That is really the hundred million dollar question. I suspect it depends on what exactly you want. I'm optimistic that we can get something useful on-line for the end of 2012 or early 2013, but that of course depends on community involvement and help. We will be shipping our gtk3 support in 'experimental' mode for people to try out for 3.5.0 which should be out just after FOSDEM. The Android port, I suspect, will start with a high-fidelity document viewer, with that evolving over time to allow editing. Of course, there is some unpleasant proprietary Apple tablet and phone operating system that we may want to re-target some similar work towards too.
> As always the punch line is that everything goes quicker if more people help out, so that we can bring these expertly guesstimated dates a lot nearer; tell your friends.
There are some other online spreadsheets, like a TWiki module, but they're not great.
I haven't paid as much attention to PowerPoint compatible online presentation software; I think EyeOS or FengOffice may have to do for now. (Isn't OpenGoo, Feng's old title, a much better name?)