Remember that problem of using Chrome extensions from the Google Web Store? You're going to have an even bigger issue when you want to download from YouTube using an Android app from the Google Play store, where Google has an even tighter grip. (Nor can you actually download anything with your officially sanctioned YouTube apps. Unless you live in India.)
Carbonite's lowest tier plan, Safe Basic, runs $6.00 /month ($71.99 /year). There are two higher tiers available as well, called Safe Plus and Safe Prime, and run $9.34 /month ($111.99 /year) and $12.50 /month ($149.99 /year), respectively. Each tier is a bit cheaper if two or three years is paid upfront. Plus, they each have a few extras over the base service like external hard drive and mirror image support.
Bitcasa Infinite Drive is relatively new, but it's one of your favorite cloud storage providers in general, mostly because they offer virtually unlimited stroage for syncing and backups. When we say unlimited, we mean it—some of you are using terabytes of storage with Bitcasa. It's not primarily a backup service though, and while it was built for file syncing and storage, the Bitcasa desktop client does support regular file backups. Bitcasa supports Windows and OS X, and encrypts all of your files before uploading so they stay safe from prying eyes. Bitcasa even keeps revision history, so if you've backed up a file multiple times and need an older version, you can pick it out and restore it. Plus, you can use the Bitcasa mobile apps for iOS, Android, and Windows Phone to access your data on the go.