^^^^^
0. Titanium Backup
1. CPU Sleeper -- To switch off all-but-one core of multi-core processor equipped phones to save battery life
2. SD Speed Increase -- To increase cache of SD card to get speedier access
3. RootExplorer (Paid) -- Advanced file manager which uses Root access effectively (FREE alternative is ES File Manager)
4. ROM Manager -- To flash CWM recovery and custom ROMs
5. AdFree -- To block Ads
6. DNS Changer -- To change DNS server address to OpenDNS or Google_DNS address
7. Barnacle WiFi Tether -- For WiFi tethering (usually operator's phone comes with this feature locked)
8. GameON (Paid) -- Save your game score or Load other's score to your games
9. UnDelete -- Undelete the recently deleted files
10. Voodoo OTA Root Keeper -- To temporarily UnRoot and restore root after OTA update
11. Prepaid Widget PRO (Paid) -- To show the result of USSD codes as widgets
12. SetCPU (Paid) -- For overclocking and/or undervolting CPU for performance/better battery life
13. ClockSYNC -- To Sync your phone's Time very accurately
14. NTFS Mounter -- To mount external drives using NTFS file system via OTA cable
15. RootCallBlocker (Paid) -- (Not working for DualSIM phones)
16. RootBooter (Paid) -- To reboot to Recovery/Download mode/just reboot
17. VoiceRecorder (Paid) -- Some phones (Eg GNexus using AlsaMixer) needs root to record both side voices
18. APK Uploader for Root -- Backup the installed apps' apk files
19. Calibrate Battery -- To re-calibrate phone's battery
20. Market Enabler -- To see apps not to be listed for your country
21. Internet Firewall -- To prevent some apps to access internet
22. Tasker (Paid) -- To automate tasks simply and effeciently
23. WiFi Connection Fixer -- Fixes "Avoided poor Internet Connection" error in some ROMs, useful if you use your WiFi in ground floor on first floor
24. Camera Sound OFF -- Useful for phones where cam sound can't be disabled
25. Light Flow -- To show different lights from the Notification LED lights for different events
These are some of the root apps useful for beginners and still there are sooo many advanced root apps available and I have NOT listed few apps like LCD_Density changer, Kernel Tuner, Font Updater that are NOT useful for most users.
Further some apps may overlap the function of other apps. Please see review and use them.