Recently I got a Galaxy S III from AT&T at my local Best Buy...They were going for $49.99 USD and I couldn't resist, especially since I've been out of contract for a year and it was time for an upgrade from my iPhone 4. (Which is still a good phone BTW, I just don't like the lack of customization) The First thing I did was root the phone, by flashing through Heimdall and the installed Clockwork Recovery on the phone. After performing a backup, I installed the CyanogenMod 10.1 NIGHTLY Rom. I was not impressed with Samsung's TouchWiz and I knew I wanted Vanilla Android on my device, hence I did this.
After installing I set up my device and apps, and I've got to say I love the phone, It runs fast and is very customizable. Since I modded, I no longer have access to S Beam or the gestures, but I never really cared for that stuff anyways, what I wanted was a fast usable phone and CyanogenMod 10.1 did it for me.
Here are some screenshots of the phone running two version of 10.1 Nightly, The bottom one is my current setup as of today.