YES, I would argue that a device is not even worth using without root. Root gives you total control over your system allowing your device to be more customizable. With root alone you can use apps like:
titanium backup - backup apps, remove bloatware, create flashable zips, freeze system services, and everything else involving app management.
xposed framework - a framework with modules that give control over android which rivals many ROMs.
Busybox - gives slimmed down version of gnu core libs on android, more advanced alternstives like gnu core libs have also been developed
Botbrew - install a minimal debian over android , adds dpkg/apt support.
GMD gesture control - replace navbar with gestures and create gesture shortcuts on android
Overclocking - Need I say more about how much faster you could make an already fast device?
Adaway, adfree - Quite a few root adblockers
AFWall - block apps from having internet access
Xprivacy module - block all permissions or feed false data.
Gamekiller - can be used to change memory values for game credit integers. Unlimited gold in apps with in app purchases.
DSploit - metasploit for android
Those are just a few things you can do.