[Sprint Samsung Galaxy S III] cypher_zero:
First off, let me say that I did not develop this schtuff and all thanks should go to those that did. Special thanks to noobnl (his thread here), mskip and TeamEpic for all their work.

A note about these instructions:

They're long and may seem a little daunting to those that aren't experienced. Please don't let that deter you as they've been written to be as simple and easy to follow as is reasonably possible assuming you can work a Windows PC and extract a zip file.

==> If you encounter problems with these instructions, please check the FAQ in the post following this one. <==

For video instructions (courtesy of qbking77) scroll to the bottom of this post.

Non-ADB Root instructions (Windows Only):

First, the non-dangerous, standard user stuff:

Download and install the Samsung USB drivers from Samsung's website: http://downloadcenter.samsung.com/c...nt_L710_GSIII_Samsung_USB_Driver_v1_4_6_0.exe

Turn on Debugging on your Phone

Open Settings

Select "Developer options" in the System section

Check the box for "USB Debugging"

Press "OK" to confirm.

Plug you phone up to your computer using the USB cable and allow the drivers to install.

Download CMW_SuperUser_v3.07.zip from the bottom of this post

I recommend making yourself a nice little GS3 folder in your downloads folder for all this stuff so it's easy to find

DO NOT UNZIP!!

Copy CMW_SuperUser_v3.07.zip on to the Root of your GS3s INTERNAL storage (if you put it into a folder, you may have a hard time finding it later, but that's on you).

DO NOT UNZIP!!

Unplug your phone

Power off your phone

Now, this is the part that can BRICK your phone so follow ALL instructions CAREFULLY!!

Download Odin3-v3.04 from the bottom of this post

Extract Odin3-v3.04 into it's own folder somewhere where you can easily find it.

Download clockworkmod.tar from the bottom of this post to somewhere you can easily find it.

Reboot your phone into download mode

Hold down Volume Down, Home and then the Power button until the Warning!! message is displayed

Press Volume Up to continue.

Your phone should now be in download mode, displaying a green Android and say Downloading. If it is not, power off your phone by holding down the power button and then try to get into Download mode again. Do NOT progress until you have done so.

Go into the folder you extracted Odin3 into and run Odin3 v3.04.exe (you may have to Right-Clik => Run as Administrator)

Connect your phone to your computer via USB. Drivers may install again; if this happens, allow them to finish before progressing.

In Odin, the COM box all the way to the left should turn blue and it should say Added!! in the Message area.

Click on PDA and in the Open window that pops up navigate to and open the clockworkmod.TAR file you downloaded earlier

Verify that Auto Reboot and F. Reset Time are checked

Click Start. Once the process is completed you device should automatically reboot and there will be a green PASS! box in the upper left of the window. You can then close Odin.

Power off your device and boot into Recovery mode

To boot into Recovery mode: Hold down Volume Up, Home and then the Power button until the device begins to power on then release all 3.

You'll know you're in recover mode when it says "CWM-based Recovery" at the top of the screen

Install CMW_SuperUser_v3.07.zip that you copied onto your internal memory

Navigating ClockWorkMod Recovery: Use the Volume Up and Down rocker to change the highlighted option and the Home button to select an option. The Back softkey works, but will not be lit and will take you back one screen.

Installing a zip:

Select "Install zip from sdcard" (Yes, I know it's on the internal storage.)

Select "Choose zip from sdcard"

Select the zip you want to install; in this case CWM_SuperUser_v3.0.7.zip

Select "Yes" to begin installing

Once the process has completed use the Back arrow to get back to the main recovery screen (Remember: it works, but it's not lit) and select "reboot system now." Once your device boots up you should now be 'Rooted,' but there's still a few more things to be done

Install BusyBox. There are actually several ways to do this, but the BusyBox app in the Google Play Market is quick and easy.

Install BusyBox (this is a link to the online verison of the Google Play store. You can actually follow this link and install it from there and it will get pushed to your phone. Alternatively, just search for BusyBox in the Google Play store and it should be the first app in the search results from author Stephen (Stericson))

Open BusyBox Free from your App Drawer

Allow it Root access when it prompts you

Tap the red "X" to close the dialog window that pops up

Allow BusyBox to scan you phone

Tap "Install" to install BusyBox and make the necessary file changes.

Update your Binaries.

Open the Superuser App from the App Drawer

Get into settings (the wrench icon in the upper right of the screen)

Select Su binary under the General section towards the bottom of the list

Select Update

Your device is now rooted and all set.

How to video (YouTube): http://www.youtube.com/watch?v=7Soapch0c5U

Thanks again to qbking77 for the instructions video!

P.S. If you are a developer or I have used some of your material and/or you feel you should be credited, please let me know and I will update this post.