Titanium Backup Root is a decent backup app with plenty of speed, but it only works on rooted Androids. The app doesn't even let you test its backup if your phone isn't rooted. However, if your device is rooted, you might enjoy this app's straightforwardness and all of the features it offers if you opt for the Pro version.
This app backs up all of that data on your phone and SD card, including your app data. It can even back up system apps and move them to your SD card to save space. The only catch is that Titanium Backup Root doesn't do anything on a standard Android without a root. The app goes to work quickly and only took a few minutes to back up our entire phone during testing, which is impressive. The app's Pro version is where most of the advanced features come into play, though. If you upgrade, you can do multiple backups for each app as well as schedule as many backups as you want. The Pro version also allows you to sync your backup with online storage, like Google Drive, Box, or Dropbox, even though we would expect this to be standard in any backup app.
The free version of Titanium Backup Root isn't a bad app by any means; you're just probably better off going all in on the app and buying the premium version. It's fairly priced and has a bevy of advanced features that rooted users will love.
From Titanium Track:
You can backup, restore, freeze (with Pro) your apps + data + Market links. This includes all protected apps & system apps, plus external data on your SD card. You can do 0-click batch & scheduled backups. Backups will operate without closing any apps (with Pro). You can move any app (or app data) to/from the SD card. You can browse any app's data and even query the Market to see detailed information about the app.
What's new in this version:
Improved Market link backup/restore/detach: better support for recent versions of Play Store app.
Improved UI layout (icon dimensions and other minor things) on Full HD devices (eg: Samsung Galaxy S4, HTC One).
Fixed hang when restoring externally stored apps on a device with no SD card.
Fixed failure to restore Wi-Fi networks from XML on some devices (eg: HTC One).