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). However, installing CWM requires a bit of ADB and command line use, so if you're not comfortable with that, you might want to wait a little while longer. The full instructions can be found via the source links below.
Of course, this root has been achieved before Verizon has even managed to get the device in its own stores. This leaves us to wonder why they even bother locking the device down at all, if the lockdown methods are so ineffective. Ah, well. Such is the way of the carriers.