Models: SGH-T999, SGH-I747, or SPH-L710 (US/Canada)
Edit Update: Here is the best working new guide I have found
http://androidroots.com/how-to-root-samsung-galaxy-s3-easy-for-att-sprint-t-mobile-rogers-carriers/
I followed the instructions for this link in the ATR thread http://forum.xda-developers.com/showthread.php?t=1726960
It didn't work for JB on the S3 for me. I found a more updated guide guide here: [link removed, see end of thread]
Edit Update: Here is the best working new guide I have found
http://androidroots.com/how-to-root-samsung-galaxy-s3-easy-for-att-sprint-t-mobile-rogers-carriers/
I followed the instructions for this link in the ATR thread http://forum.xda-developers.com/showthread.php?t=1726960
It didn't work for JB on the S3 for me. I found a more updated guide guide here: [link removed, see end of thread]