Rooting the Verizon Moto X has been proven possible in the past, however a patch for a previous exploit was released with a recent over-the-air update. But in the always fun to watch game of cat and mouse, the rooting community has stepped forward with another option for Verizon Moto X users looking to have a rooted handset. This one comes by way of jcase and will work even with the most recent camera software update in place.
That being said, while this is available and can be done -- the process is not one that everyone is going to want to tackle. To that point, event the folks at RootzWiki have described it as being "not for the faint of heart." There is a long and complicated set of directions, and in addition, you will need adb installed on your computer.
Just to clarify, you will also need to know how to use adb. Not to mention, be comfortable with telnet as well. With that we suspect some have decided to keep their handset the way it is -- non-rooted. But those who feel the need to have root, make sure you proceed with caution and read everything a few times before beginning the process. Better safe than sorry.
Anyway, while we aren't going to list the full run down of steps here, we can say things begin by installing a program called Cydia Impactor. From here you find the IP address of your phone (using adb) and the use that to pushy the exploit to your device. After that you use Cydia Impactor to telnet into your device and get this, run the exploit three times.
It was said that each time you run it you will be given a different result -- this is one point where carefully reading the directions will come in very handy. Otherwise, from that point you wait for su to install and then move onto running SuperSU from the Play Store. And during all this, hopefully nothing locks up or goes wrong otherwise.