A good way to manage secure, automatic backups is through the established
Spideroak storage service.
They give you a good 2 GB for free, much like Dropbox, and they also offer free sync and automated backup services.
But what I like so much about Spideroak, is the fact that
not even the employees have access to your stored files. Unlike Dropbox, which plainly states in their Terms of Service that all they hold rights to use any material you upload to their servers, Spideroak stores all your files in encrypted server-side containers. It is much like a remotely mounted Truecrypt container, and only you have the key to access it.
I probably sound like a salesman at this point, lol. But pretty much if you have 25 meg of ram to spare on the machine with your wallet, it's one of - if not
the - best backup solutions out there. The only functional backup & sync service out there that I know to not skimp on the security at all. Not one Bit. (hurr, pun)
Did I also mention it has native Linux support with packages for multiple distros?