Motorola's newest DROIDs have only been out for a couple weeks now, but the folks over on XDA Forums were hard at work to see who would collect the $830 bounty. As it turns out, user "jcase" was the first to successfully develop a rooting process that would work across the Motorola DROID MAXX, Ultra and Mini.
Now you should be aware that you will need some knowledge of using the ADB Shell, so if you aren't comfortable with that, you may want to hold off. But other than that, it is a pretty simple process. Unfortunately, the Bootloader remains locked, so you can't install a custom ROM or Kernel, though we are hopeful that the Bootloader will eventually get broken as well.
Here are the instructions, as provided by "jcase". And at always, use at your own risk.
Update 9/13/2013 - Version 1.1
Download the MotoRoot app Version 1.1 (download link)
Install the downloaded file by typing "adb install -r MotoRoot1.1-Droid.apk"
Then run the MotoRoot app on the phone, and click on the Setup button.
Phone will reboot, and will now be rooted.
Download and Install the modified SuperSU version 1.66 from here, as the one from the Google Play store is not compatible.
Uninstalling the app will disable root until reinstalled
supersu is not able to update su yet, this will be fixed in an update shortly.
su is maintained in a ext4 img at /data/xbin.img and mounted over /system/xbin at BOOT_COMPLETE.
su is not available for the first few seconds of boot, im working on this.
/system is write protected, even with unlocked bootloaders you can not write to it while booted in Android.
Two choices, factory reset, or press the unroot menu option in the app.
Here is a YouTube video showing the process:
For even more in-depth tech details of how this rooting process came to be, check out the Android Police link below.
source: XDA, Android Police, and YouTube