Not locally: I've seen many organizations admire the synchronization and collaboration features of GDocs, with a major caveat: the data is centralized in the cloud provider's hands, not the organization's. "Oh look, you don't own your data anymore" is a very theoretical scenario, but "oh look, you suddenly can't access your data anymore, we're not bringing them back, and you have no recourse" has happened with many cloud storage services, for various reasons.
Hosting your own network-based office web-app solution would be convenient for many...especially for the security.
If organizations rely on google docs so much, why don't they back up their google docs archive every {day,hour,minute} ? I'm sure there's an rsync for google docs or something.
Having to revert back to emailing saved word documents for a week or two is far better than losing everything for a week or two.
I want to share docs with the internet, or with a small team, have integrated history, have instant editing, have the possibility of more people editing it. I want to have instant access to it from any computer with a browser.
You could probably extend wikis like mediawiki to have live visibility of edits, at the cost of performance. Separate db or redis storage for in-progress edits, and query that before retrieving the last static version of the page...
Hosting your own network-based office web-app solution would be convenient for many...especially for the security.