I'm not rooted. Don't see the need. I'm happy with the way the phone works. We got JB relatively quickly.
I did root my old Captivate for three reasons: (1) because it refused to update to Gingerbread (Kies on old Mac didn't work for ****); (2) so I could have Swype Beta (it came with some ungodly old version of Swype and wouldn't let me have both); and (3) because the GPS sucked monkey butt and I wanted to tinker with it to see if I could improve it (I couldn't, btw). With the S3, I can have both official Swype and Swype Beta installed at the same time, I have official JB, and the GPS is perfect.
One bit of caution with rooted phones: some apps are written not to work if your phone is rooted. I believe you can't watch videos you rent/buy through Google Play on a rooted phone And if you ever want to use ISIS, Google Wallet, or some other NFC payment technology, I'm 99.9% sure those apps will not run on rooted phones (for obvious security reasons). Plus, with root access, you literally have access to everything on that phone...so if you delete something by accident, you can render your phone inoperable.
Actually wallet works perfectly fing on rooted phones. and you can watch movies with play movies.