It's a regular rite of passage for new Android phones: most flagships get the root treatment within a day or two of being released, allowing power users access to tools and apps that most people aren't all that interested in. But there are some exceptions, namely those draconian carriers who insist upon locking the bootloader of their Android devices. Their reasons for doing so could charitably be described as "bull hockey," but they're pretty effective: it's sometimes months or years before these phones get rooted, if they do get rooted at all.
Not so with Samsung's new pride and joy, the Galaxy S6 and S6 Edge. An intrepid group of modders has managed to root a handful of variants, including the locked-down Verizon and AT&T models of both phones. Check this XDA forum post for downloads and instructions for "PingPong Root" from Keen Team. It's fairly simple if you're an experienced Android ROM user - it doesn't even require a PC, just download the attached APK files and follow the six-step process for obtaining root permissions.
What's even more impressive is that because this method doesn't use Samsung's ODIN flash tool it shouldn't trip the KNOX security feature installed on all new Samsung Android hardware. That means that secure apps like Samsung Pay and My Knox should (should) continue to function even after applying the APKs.
Of course, nothing is guaranteed with this kind of hacky method. I'd recommend carefully reading through the entire first post on XDA, checking your ROM version against the compatibility list, and using XDA's thread search tool (in the upper right hand corner) to look for any potential problems with your particular model, carrier variant, and software version. Also: remember that as of Lollipop, any changes to the System partition of Android will cause all OTA updates to fail. Ready to go? Then head over to XDA to give this root method a shot. Video instructions have been uploaded to YouTube here and here.