Camera shortcut:
Twist the phone (as if turning a door knob back and forth) and it turns on the camera - even if the phone is off. I find myself trying to launch the camera on other hones like this!
Touchless controls:
Launching Google Now when the phone is off by saying "Ok, google Now" and then getting it to call/text people (among many other tasks) is very useful to me when I am biking and can't use my hands.
Active display:
This is the best one for me. If the phone is off and you pick it up, or turn it over, or pull it out of your pocket, etc., it will display the time, and any notifications. pressing and holding the notification will show the notification itself. Swipe up to go directly to the notifications app, swipe down to unlock the phone to the home screen, or swipe sideways to ignore it.
Motorola Connect:
This is a Chrome extension that allows you to text from your computer. ther are other apps that do this, so it can be replicated on other phones.
Motorola Assist:
Automatically detects when you are driving, and can do preset actions (reading out texts and announcing callers, play music, etc). It can also change settings when you have meetings on your calendar (so your phone automatically goes o silent and doesn't ring) and you can create a sleep/awake schedule which also changes settings.
This can also be replicated on other apps, but not as simply as Motorola Assist does it.