From the developer behind the needs-no-introduction Rom Manager comes a new backup solution that not only syncs apps between devices -- it brings the app data long for the ride as well. Carbon (yes, it's called Carbon) uses Android's built-in backup feature and has several syncing options (or will at some point), but right now Google Drive's the way to go for cloud syncing. The gist is you can back up apps and app data from one device, and restore it on other. No muss, no fuss, mostly. But do remember that this is beta, so things are missing/wonky.
Carbon needs root access in this beta form (which will only work for a week, Koush says), but the finalized version should work on non-rooted devices, so long as they're running Android 4.0 and up. Hit the link below for more and to download the beta.