1. Greenify
Greenify is one of my favorites. As you know, most of the apps in Android run silently in the background and hog valuable resources on your phone. With the Greenify app, you can quickly hibernate any/all the apps that are running in the background. The good thing is you can also use Greenify on non-rooted devices (experimental feature).
2. Root Uninstaller
Most Android phones suffer from pre-installed bloatware, and there is no easy way to uninstall them unless you root your device. To uninstall all the bloatware and crapware, just install Root Uninstaller and you have your work done. Of course, be careful while you are playing with Root Uninstaller as uninstalling any required system app may break your Android device.
3. Tasker (Premium)
Tasker is a simple yet powerful Android automation app. While Tasker looks scary at first, it makes your smartphone even smarter by automating various tasks, be it simple or complex tasks. For instance, if you want to turn on your Wi-Fi automatically when you reach home, Tasker can do that. Want to have a regular automated backup of your SD card? Tasker can do that too. These are just a few examples, and once you get it and get used to it, you will definitely love it.
4. Trickster MOD Kernel Settings
Rooting your Android device allows you to do a lot of interesting things like clocking your CPU or GPU, controlling fsync, etc. Trickster MOD Kernel Settings is a straight forward app that has a ton of options to tweak your Android device as required. But beware, this app isn’t intended for beginners and any wrong configurations may cause problems with your device.
5. AFWall+ (Android Firewall)
Android, by default, gives you very little control over how you can connect to the Internet, i.e. you cannot pick and choose which app to allow or disallow the Internet connectivity. Using AFWall+ you can easily configure which apps can connect to the internet while being able to control traffic within LAN.
6. DriveDroid
Having a Linux USB stick with you helps when in need. If you don’t want to carry an extra USB stick, you can easily install a Linux operating system right in your Android device using DriveDroid. You can attach your Android device to any PC to have your own booted Linux operating system whereever you go. DriveDroid is also available as a paid version with some extra features like resizing images, ad-free interface, etc.
Hopefully that helps, and don’t forget to share your favorite root apps down in the comments form.