My regularly used ones are
Whatsapp
flipboard
ZDbox -- used to kill running process, clean cache, get detailed battery status, applock, batch move to
SD Card etc.
Colornote - nice checklist
Appsaver - Easy backup apps to SD and install when needed
Titanium Backup - A complete backup tool for root users, gives you wings to backup/restore in details.
ES file manager - root explorer
Es Task Manager - using it only to edit the startup apps
Bagrounds HD - Nice HD Wallpapers
Drive -
Google Drive
Paytm - Mobile recharge
compass leveler - as the name says
missed call reminder - reminds of missed calls and SMS using custom tones
mobile backup II - helps sometimes restore
MX Player - ultimate video player needs to justification
Quickboot - helps me restart as stock power menu doesn't has reboot
Screenshot everywhere - no bullshit but pure screenshots using a touch
Shaplus Caller Info - shows operator names of incoming/outgoing calls
Quickpic - Best Gallery App
Stop watch and timer
PNR and Rail Info - good for most of railway lookups
A firewall blocker - was sick of vodafone sending me "Khas aapke liye" types bullshit even after full DND, its now gone to bin.
Camera ICS : lets you take the Shots Silently
and the best 2 Apps to Tweak and improve your battery run time.
1).
Lux, It lets you customize or use pre-defined level of brightness for screen,
it actually adjusts the brightness on the fly so you can more comfortably view the screen if you spend many long hours with your screen.
2).
Greenify - hibernates Apps after a certain amount of time, this will drastically improve the battery backup for your
android device, as initially my phone was doing 1+ day, but after 80+ user apps the battery was kinda draining heavily even if I used only a couple of them,
with greenify I no longer worry no matter how many app you open and close, it would take care of them automatically.
however to be on safer side and be connected I exempt gmail, maps, zdbox, missed call alert, lux, shacaller info. so these apps are only things running on my phone 24x7.