SpiderOak is well known as one of the most privacy-centric cloud storage services, but it's also a great backup service. The same power and features that you get for file syncing and access extend to its backup client, and SpiderOak's "Zero Knowledge" policy extends to your backups as well. Even they don't know what you're storing on their servers, and all of your data is encrypted on their servers and before it leaves your computer. The SpiderOak desktop client has a fully-featured backup tool in it that lets you back up your entire desktop, documents, email, music, or movies right to the cloud, or you can hit the "Advanced" tab and pick the files and folders you want to save, including external drives, network drives, or anything else on your computer. As you add files to your backup job, you'll get a live preview of how much space you'll use with what kinds of files, and whether you have space for it. SpiderOak supports Windows, OS X, and Linux, has mobile apps for iOS and Android, can do incrementals, and if you uncheck a file to stop backing it up, the files will still live in your SpiderOak account, just as an archive. Your backups happen in the background, or when you schedule them.
CrashPlan is completely free if you're just doing local backups, but even online backups are affordable, with CrashPlan+ accounts starting at $2/mo (per computer) for 10GB of online backup storage, and going up to $4/mo (per computer) for unlimited online backup storage and $9/mo for unlimited online backup storage for a whole household. You can check out their plans here, and try them free for 30 days with a new account.