I have heard the ringing also in my Droid Razr. The phone was in my pocket when I heard the ringing. I am a school teacher so, of course, I thought it was a student's phone. It sounds like the digital version of an old fashioned alarm clock bell but rings, in the ear piece only, like an incoming call (i.e., rings for approx 2 seconds and then stops, repeats). I turned my phone off then on and it stopped. I only heard it when my phone was unlocked and like a previous post said when I went to turn it down it was "incoming volume" but with no phone call was made. If anyone knows the cause of this problem I would love to know. It has only happened once...so far.
Other items of note: my backup assistant had failed and my data signal was nonexistent. My phone works on 3G when inside the building and I do not have my Wifi on.