Although there have been a few lucky individuals that have received their device or will be receiving it tomorrow, the Samsung Galaxy S III for Verizon has been a tough device to get a solid release date for. It was initially supposed to be released by the first week of the month and now it looks like future orders for the handset will not ship until July 19th.
Verizon has also chosen to be the only carrier to lock the bootloader on the device. That makes flashing custom firmware to the device a pain. We have heard that you can still root and flash custom kernels to the device but I would hold off on doing that for a while. The official in store purchase date has not been announced yet.