Why to root in general...
1. Back up app data. Like your hard earned score on Angry Birds.
2. Theming
3. Back up SMS Messages
Why to root the Note 2...
4. Have the ability to turn on and off the Camera Shutter Sound.
5. Add Call Recording Feature
6. Add like 20 other features, example: Call Log timer, Messaging settings (Signatures, themes, reminders, and more), Take a picture while in a call, play music while taking a picture, Reject Option in contacts. All simple settings you can easily change that really should be on by default.
7. Because all the other kids are doing it!
8. Multiwindow Mod (Allows you to open any app with the Multiwindow feature.)