Here Is a List of Roms/Kernels/Mods/Tweaks for your AT&T Galaxy SIII i have tested most of these and i will add a * to the ones i have tested.
DiscalmerI am not responsible for any Damage Done to your Phone.
If it explodes or self destructs i do not take any responsibility.
I am not the developer of any of these Roms/Kernels/Mods/Tweaks
show your appreciation to the developing community and go hit there Thank button or/and Donate
CREATE A BACKUP I RECOMMEND THIS 100% BEFORE YOU TRY ANYTHING!
YOU HAVE BEEN WARNED
*Ultimatum Rom- this is by Far My Favorite Rom I have Used it is based on Stock. It is Debloated, deodexed, zipaligned, and pre-rooted. This is a heavily Debloated Rom Anything that is AT&T or is Samsung. HERE is the official site.
*CM10 (Official)-IF you want JellyBean and want Vanilla Android this is your Rom. This is the Official Cyanogenmod 10 for the S3. It was Developed by Cyanogen himself. This Rom Still Has things Broken but is Working Really Good and can be used as a Daily Driver.
Diet ICS is a rom based on stock. it is Debloated, Deodexed, Zipaligned, Modded Power menu, CRT-off animation (flickers). This another Heavily Debloated rom.By: jdbeitz
KyanRom is a Debloated rom has Native Tethering, Wallpaper Scrolling Mod, and also a 50GB of DropBox Bonus.
Nostalgia this is a deodexed, compacted, and zipaligned rom. this is a great rom if you want faster phone, and better battery life.
TuchMi S3X Debloated, Pre-Rooted, Busybox, Goo Manager Compatible, OverClocked (1.8), Battery mod, Supercharge Script. Great Rom Based on Stock.BY: smokin1337
*RESSURRESCTION this is rom based on Stock but is super tweaked with a ton of extras. it is also OverClocked up to 1.9!. also 15 toggles.
BY: Team Insomnia
AOKP this is one of the most known and leading roms out their. this is based o ics and if you want gapps you will have to install them. This is an Unofficial Variant of AOPK but still work Great.
BY:Task650 & Ktoonesez
CM9IS one of the Most Known ICS rom out their. This rom still has some issues so make sure you read them before you install it.
Paranoid Android If you what your phone to be a Phablet This is the true Hybrid without having to multiple Mods. This is based on Jellybeans and still has some Bugs some make sure you Read them. This is not turning your phone in to a Tablet its turning it in to a Phablet for those that don't know its a combination of Phone+Tablet so its the best of both worlds
KT747* Kernels There are multiple kernels for stock, AOSP ICS, and AOSP JellyBeans.
V6 SuperCharge Great mod/Tweak will help with Kernelizer, 3G TurboCharger, and Die-Hard Battery Calibrator
Google WalletI know People are bummed that the only US S3 model working with Google wallet is Sprint. Well Here is how to get it and join all those people who get to pay with their phones.
Google Now* for all who are waiting for Google Now and/or Hate S-voice here is how to get it. and i got to say this is a must have mod if you like using all these types of apps.
If you have any other rom/Kernel/mod/ or Tweak i have not included add it below and i will add it to the list.
if this helped dont forget to hit the thank button :smokingsomb:
Also i would like to thank kool kat2 for his Suggestions
Happy Modding to all