1. Choose what is installed.
The first benefit of rooting your Android device is full control over the applications installed on your handset. No longer do you have to suffer from the cluttered app drawers and reduced memory space taken up by pre-installed carrier and manufacturer applications, you can instantly enhance your memory by uninstalling what you don’t need and keep only the apps that you really want.

2. Improved backup and restore options.
Yes, the cloud can back up some of your settings and app downloads, but that is not really a true backup; it’s just a list of things for the phone to download and change. Want to keep everything the way it was? You will need to root.
Titanium Backup is one of the most popular backup apps used by rooters, and this, or a similar app, is essential if you’re going to start tinkering around with Android software. But as well as acting as a safety net in case you uninstall something important, Titanium Backup can also be used to back up your user data… any and all user data.
3. Updates as they come
Manufacturers are often slow at delivering the latest Android versions even to their flagship handsets, let alone aging devices. Some are getting better at it, but this is still an ongoing issue for many users. So if you’re not a Nexus device owner, rooting opens the door to much faster Android updates, thanks to the developers who put time into porting the latest updates to various handsets.
4 .More Apps
As rooting opens up administrator type privileges on your handset you’ll instantly have access to all the core files on your handset. File browser apps can take full advantage of this, allowing you to move stuff around on your internal memory if so require.
App wise, we’ve already touched on Titanium Backup, but there are far more apps that can make use of root permissions, and simply aren’t available with a non-rooted device. Fans of custom ROMs can even use a ROM manager to install and update their operating system without the need to flash zip files from Recovery.
5. Customize to fit
Although there are options to tweak themes that don’t require rooting, usually through third part launchers such as Apex and Nova, rooting gives you access to the important files needed to make changes in folders that are usually hidden from users. Access to the /system/fonts folder allows users to install and replace custom fonts. You can also flash zip files from Recovery to install themes too. But if all that folder browsing isn’t for you, there are also some great root-only theme applications to choose from.
Source http://www.timigate.com/2016/02/best-reasons-to-root-your-android.html#more