This happened to me, just now.
I was surprised to hear the ring because it was so soft, a tone that I didn't recognize as a DROID ring, and because my phone was set to silent, not even vibrate.
First, I checked to see if I was receiving a call. Nope. Next, I looked in my notifications menu to see if it was from some app. Nope. I decided to open what few apps I had to check if I had unread notifications. Nope. Changing the ringer volume via the sidekeys did not change the volume of the audible ringing tone.
I searched online and couldn't find anything on the issue. I did, however, receive a message on Twitter of something similar happening to someone else, so I came here.
Though there appears to be no official release on what this phenomena is, I would hope that enough of us reporting it will urge Verizon, Motorola and/or Google to look into it.