Dropbox as a CMS - DropPages
droppages.com
droppages.com
Back then we did it the hard way basically making our own Dropbox API. We had a Windows server running with the Dropbox client installed. You would share a folder with our Dropbox username and our script would auto accept it, and then we ran rsync to sync up the Windows folders with our web servers. Back then getting the Linux client to run was a bit of a pain which is why we went the windows route for that part of the site.
Someone is bound to open source something similar to allow you to self host, thus bypassing droppage's revenue model to some extent, but for non-techs (or just-a-bit techs), this is stellar.
For simple speed to up and running a kosher, reliably backed up web-site, this is hard to beat.