There might have been moments before when you took your phone on a trip with you to a country where there only GSM networks in use, hence making it a problem to use your CDMA based phone. The Verizon Galaxy S3 is also a CDMA/LTE phone with no support for GSM networks. Well, at least not officially.
A hack has been discovered for the Verizon Galaxy S3 that lets it be used with GSM networks, making it a true world phone so to speak. XDA Forum Member lair12 has posted the steps required to enable the phone to use GSM networks, which he personally tested on a trip to Russia and mentions that it should work with any Europe SIM cards (GSM is common all over the world so it should in theory work on any GSM network). There is a hack for both switching to GSM from LTE and then switching back to LTE again.
However, the procedure does involve hacks like rooting as well as flashing a custom recovery image, so one should proceed with caution before trying it out. Head over to the XDA page where the hack is posted for the full step-by-step instructions. If all works well, those overseas trips should be less problematic.