You can try this: http://www.cloudhq.net/dropbox
Additional to sync, you can browse, copy/move, and edit dropbox document directly from Google Apps window. And there is also backup of Google Docs into Dropbox.
With cloudHQ for Dropbox browser extension you can manage (browse, copy, move, and edit) all your Dropbox files and Basecamp projects directly from a Google Docs interface. Furthermore, cloudHQ for Dropbox will continuously synchronize all your documents between Google Docs, Basecamp, and Dropbox. And, cloudHQ can also protect all your Google Docs files and Basecamp project against accidental and malicious deletion: cloudHQ can backup multiple Google Docs accounts and Basecamp project to Dropbox.
cloudHQ features:
- copy files between Google Docs, Basecamp, and Dropbox directly from Google Docs interface
- browse and view Dropbox files and Basecamp projects directly from Google Docs interface
- backup of multiple Google Docs accounts and Basecamp projects to Dropbox storage
- continuous synchronization of multiple Google Docs accounts and Basecamp projects with Dropbox storage
- edit Dropbox files and Basecamp project attachments directly from a Google Docs interface
More info: