Of the four major US carriers to receive the Galaxy S III, Verizon is the only one to lock down the bootloader. This has made a lot of people very angry and been widely regarded as a bad move. Nevertheless, enterprising hackers over at XDA and RootzWiki have successfully managed to circumvent the lock, achieve root, and flash ClockworkMod recovery. If you're on Verizon and anticipating owning a Galaxy S III, congratulations: your phone is yours again.
The process is laid out on both sites. Achieving root seems to be a fairly simple process if you're familiar with Odin (a common, easy-to-use tool for flashing Samsung devices).