Check out iQ Android Recommend Android Apps for Root Users and Standard Users below. Click each icon for more details and to download.
Root User Apps
Purify – Silence annoying notifications and extend battery with powerful per app manager
Titanium Backup – Completely back up your android device data and settings. Online backup available in pro version.
TWRP Manager – Manage your custom ROM and custom recovery
Greenify – Extend battery with this app power manager
SuperSU – Manage root permissions
RootExplorer – Control all the files including system and hidden / network locations
ROMToolbox Pro – Includes many apps, essential for true root user enthusiast
AirDroid – Use your android from your computer, remote usage app
Standard User Apps
CleanMaster – Clear junk files and free up RAM memory to boost performance
Advanced TaskKiller – Force close apps in one tap, boost system responsiveness, kills background apps
DSBattery Saver – Extend battery to prevent dead when you are away from a charger
Signal Private Messenger – share media or attachments all with complete privacy, call feature included, no SMS or minute usage
Vaulty – hide sensitive images easily
WheresMyDroid – Locate your device with alert sound and GPS tracking
Helium – Back up android to SD card or PC
SMSBackup+ – Save all your SMS and call log to your google account, restore anytime
Root Checker – This app shows if your device has root access (does NOT root your device)
Antutu Bench – Runs a performance test for your device and give you a score you can use to compare results against other software or devices.