Development of CM9 for the US Galaxy S III is still in its early phase, and the ROM itself is said to be not very stable, although good enough for a "daily driver". But what about Verizon GS III users? As you know, Samsung announced a Developer Edition of the Verizon version, which is practically the same but with an unlocked bootloader, but in order to get one of those you'll have to pay full price ($599), as Big Red isn't subsidizing it. Plus, getting one won't even guarantee that you'll eventually get CM 9 for it, as the CyanogenMod team hasn't announced plans of bringing its software to it yet.
But, if you are a proud owner of an AT&T, T-Mobile or Sprint Galaxy S III, feel free to visit this link to learn everything you need to know about installing CM9 on your device.