You dawg I heard you like relying on the cloud for backup, so I backed up your cloud data on the cloud so you can rely on the cloud while you rely on the cloud.
Your comment is amusing, but there's merit to diversifying your cloud storage. I.e. if I lose access to gmail, I still have my dropbox stuff. Storing offline is another way to diversify, but it's subject to a lot of other vulnerabilities.
I think Greplin could provide this service fairly easily (since they are already indexing all of your data from other services for you and perhaps have access to your DropBox account.) Just using Greplin today as-is they could be a good cloud-based "backup" of a lot of your cloud-based data, so long as they do not automatically wipe out older data to match what is on the individual services.
Another service that could be really helpful for this problem would be one that would just automatically burn your DropBox account (which ideally had copies of your other cloud-based data) onto DVDs and send them to some location at some interval for automatic cloud-based offline backup. Not sure if you can automate the mailing part, though, and I would worry a little about ensuring that people get the right data.