i rooted to get rid of TouchWiz, and delete the status bar. never did like the default launcher and even replacing it left a lot of TouchWiz stuff behind (such as the stock lockscreen constantly replacing Widgetlocker as well as the TouchWiz themed status bar that had those toggles in it that could not be changed in any way). TouchWiz also takes a good chunk of memory resulting in occasional lag.
Also, never did like Android's notification area, it was constantly cluttered with icons, and, coming from iOS, i preferred app notification badges and a clean top screen, but maintaining the pull-down shade. so i deleted the status bar, and make it where i can still see the list of notifications just like in an iPhone, and with Nova Prime, i got app badges too. to delete status bar or eliminate all of TouchWiz requires a ROM, which requires root.
Another benefit of rooting is making a fixed CPU speed, for some mid-to-low-end devices who's scaled CPU speeds (by default they constantly change the speeds on-demand based on how fast an app needs to run, but this can cause occasional lag as it is switching speeds, too) this helps a lot if you want a speed to remain set. i keep my GS3 at 700MHz all the time. no lag at all.
rooting also makes it uber easy to backup your device by making it easier to get into recovery. holding down power on most devices when rooted gives the 'reboot' option which gives another option to 'reboot recovery'. in recovery it's a simple click to backup your device so in case of failure you can restore all your apps and data.