The ability to install a firewall on your phone which allows you to block or allow access to the internet on an app by app basis. Very useful when installing 3rd party keyboards which could be key logging etc. It also stops ads in blocked apps.
The ability to use automation apps like Tasker to override lockscreen patterns or PINs when you are at home and connected to your home wifi. Not that major a feature, but saves you unlocking your phone all the time. Neat.
Ability to use Clocksync app to automatically sync your phone's clock with an online atomic clock. Awesome.
Ability to use Xposed framework and its ever-increasing list of 3rd party modules. Again, awesome.
Custom roms! Get rid of all the system bloat that comes installed by the manufacturer and network provider. Have a sleek, fast, cutting edge device.
The ability to use Titanium Backup to back up your apps and data to an SDcard or the Cloud.
Ability to connect phone to PC in USB Mass Storage mode.
Ability to boot your PC from boot disk ISOs stored on your phone using DriveDroid app. Geekiness personified.
Control of your device in ways not dictated by the manufacturer/network provider.
General awesomeness.
The ability to say 'yes' if people ask you if it's rooted.
(Nobody has ever asked me that, unfortunately
)
I'm sure people can think of more reasons.