USB OTG Works!
If you have an OTG cable, you can plug it into the SGS4 and then plug a USB drive into the cable.
The USB drive (like a thumb drive) will be mounted and is accessible. YOU DO NOT HAVE TO BE ROOTED for this to work.
Any USB drive should work, as long as it gets enough power. Thumb drives don't require any extra power, but real USB disk drives probably will. Most of them come with with dual USB cables, with one labeled "power only" and if you plug that into a PC or laptop but plug the other "Power and data" cable into the OTG cable, you should be able to access your large USB drive from your SGS4.
One more way to share or transfer data!
When you want to remove the drive, go to settings, storage, and you will an option to "Unmount USB OTG storage". You will not see anything in settings, storage about OTG until you plug in a USB device.