I bought a S3 from a large volume seller on eBay. It arrived yesterday, and I was Googling for a way to unlock this phone. it turns out my phone was already unlocked (why would the seller not say this when he could obviously make more $$). However I came across this post and felt the need to clear up the air due to misinformation on the websites I have seen.
Lke I said, this phone is unlocked. I put a Simple Mobile (T-Mobile MVNO) SIM card in, powered up, and I can used voice and data (after setting up APN's). The max data speed is EDGE, but it's a function of the hardware on the phone, not because it's locked. I confirmed this on Wikipedia - Verizon phones don't have 4G frequencies used by T-Mobile, so EDGE is the best you can get.
Some other web sources say that, like with Iphone 5, Verizon agreed to unlock some of their newer phones due to an agreement with the FCC around the time these phones were introduced.
As per previous poster said, the newest Android version will unlock this phone. So download Kies, update your phone, and then you're good to go. Hope this helps someone!