Samsung was the target of extensive hate recently as it came to light that the Note 3 and other high-end devices would be sporting a new region lock designed to cut back on gray market importers. The company said the lock was only a problem the first time a phone was activated, but some users now claim to be having ongoing issues with foreign SIMs not working. Whether or not Samsung's region lock is working as intended, noted developer Chainfire has released an app that can circumvent the lockdown entirely.
The tool requires root, and has thus far only been tested on the SM-N9005 variant of the Note 3 with MI7 firmware. The app updates the network list when activated and instructs the modem to reset itself. After a quick reboot, you should be unlocked. Since this is in the early stages, it is not known if other devices will work the same way, or if firmware updates will reset the region lock. And of course, you could possibly break something messing around with root apps like this. Use caution... at your own risk, and so on.
The app costs $2.79 in Google Play, but you can grab it for free on XDA. That's also where users are working to check other Samsung devices with the region lock to see if the tool works.