I absolutely do NOT believe in "free" storage. It's simply not reliable for backup purposes. The absolute most important thing to consider is how reliable your backup is. If it's not 110% reliable, then it's not a backup.
Flickr doesn't do RAW files.
There are MANY possible backup solutions out there though.
You can try Amazon S3 as they are relatively cheap, and highly reliable.
I would go for Rackspace Cloud Storage though:
Cloud Files - Unlimited Online Storage & Data Storage Services
Now, you'd need to check out whether it's the kind of thing that's right for you, BUT, you are not likely to find anything, anywhere that approaches the level of reliability and quality that you will get from Rackspace.
Rackspace has a much better value proposition than Amazon S3. They have a better network, better CDN, and better prices even. (I freaked out when I first saw their cloud storage as it really is all that.)
From their page:
UPLOAD FILES TO THE CLOUD
Store and manage unlimited files using our online control panel, desktop software, or programmatically via the API. And even manage it on-the-go via your iPhone®, iPad® and iPod® touch.
Their cloud storage uses the Akamai CDN (content delivery network), so it's pretty much the fastest network in the world.
It's not free, but it will give you peace of mind knowing that you've got your files safely stored on perhaps the world best network with the best service provider.
(I am NOT affiliated with Rackspace. I have used their services, and from a lot of experience, I know that they are the GO TO people for reliability.)
But, that's cloud storage. You need to ask yourself if you're comfortable with that.
NOTE: I am in IT and am not a professional photographer. My recommendation for Rackspace is purely based on "data safety" from an IT professional perspective and not what happens in the photography industry.