Although Dropbox isn't a backup service, it offers file versioning, so you would think you could recover from such a situation. Google Drive also offers file versioning, but the devil is in the detail - they do delete older versions:
https://support.google.com/drive/bin/answer.py?hl=en&ans...
For RAID like protection with Dropbox and other providers, you can roll your own BRIC (Redundant Bunch of Independent Clouds). I did this using Tahoe-LAFS to stripe data across storage providers. Requires a bit of set up, has some caveats, but does work. If you use with duplicity you have versioning on top of a distributed, encrypted, redundant store.