There are people over at XDA Developers who have given the Samsung Galaxy S3 more love than usual, having discovered a method that allows one to root the Samsung Galaxy S3 in a relatively painless method. Bear in mind that the Samsung Galaxy S3 model that we are talking about here is the SGH-T999 model from T-Mobile, so proceed with caution and make sure you have the right model on hand as well.
Before you continue, here is a quick primer on what rooting is all about. When you root your smartphone or tablet, it will then enable you to make changes, access system files, perform overclocking, as well as launch apps which require root access, in addition to performing far more customizations on your handset compared to the vanilla version of Android.
To date, there were no reports of bugs and issues, so you can most probably heave a sigh of relief if you were to follow the instructions here as you root your Samsung Galaxy S3.