For anyone that hasn't rooted their S3 (or any device using the Exynos4 Chip
) yet. You can now do it without even using a PC. Due to a recent exploit that has been found you can root the device really easily.
All you need to do is side load the ExynosAbuse APK
then run it. This will install the SU app giving you root access to the device.
Once SU is installed go to the Play Store and install ROM Manager
. This app allows you to install CWM so you can flash custom ROMs.