Private alternative to Google Docs?
Solution 1:
Try Etherpad, a nice alternative to Google Docs based on Node.js. We used it in some projects with relative success.
Solution 2:
You can also try Firepad which is based on Firebase, and is server independent. Only using Javascript.
Solution 3:
ownCloud is an open source, private cloud server, like dropbox or google drive, but you can install it locally. They recently added a collaborative document editing feature that you can see in action at the top of this page: http://owncloud.org/six/
I have only briefly tested the document editing aspect, but the file archival aspect has worked great across multiple machines and platforms. Just like with dropbox, you always retain a local copy of your files.