For those of you who have Mac OSX, you can root your Galaxy S3 GT-i9300 using Heimdall. This method is pretty simple to do, a bit different from Windows method but gives you the same results.
For Windows, please see How to Root Galaxy S3 on Windows!
For Linux/Ubuntu, please see How to Root Galaxy S3 on Linux/Ubuntu!
For U.S. Canadian dual-core Galaxy S3, see this other Mac root method!
Step 1. Put your Galaxy S3 into download mode by holding down Volume Down, Center Home, and Power buttons together for about 10 seconds.
Step 2. When you see the warning screen, hit Volume Up to enter ODIN Download mode.