The Verizon Galaxy S III, which has a locked bootloader ironically, has been rooted. The best part about it, ODIN, Samsung’s software flashing program, is not required. Simply download the files to your computer, follow the step-by-step instructions and you’re good to go!
The program is still considered beta even by the developers. So take care if/when using this method. There is a chance things could get dangerous, especially if you’re new to the rooting process. Check out the thread to see what the developers and users alike are saying. Have you rooted your VZW S3? Do you want to? Let us know!