Well.

I like to root my devices so I can use it how I like.

When rooted you can run
Titanium Backup - Saved me a lot
Different ROMs -
Battery calibration
Ad Free
alogcat
1-tap clean cache


Other Apps
Parcel - Great for tracking packages
Strelok
Dropbox
Zedge
Netflix
mVideoPlayer
Dolphin browser
Amazon App Store - Free app everyday
Evernote
HandyCalc - Great calculator
Overdrive media console - check out books from your library