Amazon has announced its CloudDrive service, which is kind of a competitor to systems like DropBox, or perhaps to online backup services like Carbonite or Mozy.
The Amazon pricing model appears quite simple: $1 / GB / year. The service is positioned as a place to store your music and books and other digital media that you purchase from Amazon, and for those purposes: "Any Amazon MP3 purchases that you elect to store on your Cloud Drive at the time of purchase do not count against your storage quota."
Note that a raw storage device is not a complete backup solution, of course; a backup solution knows how to keep multiple versions of your files on the backup device, can take full and incremental backups, can restore you to a point in time, etc. So if you wanted to use CloudDrive for backup, you'd need to combine it with some of those procedures. Of course, maybe Amazon will add to the service in the future.