I hate it when it starts ringing. My phone is on silent all the time for that reason (lots of missed calls, sorry), and when I'm busy the interruptions greatly irritate me (and I'm always busy).
I have been looking for an Android app that simply turns the phone to silent when it is put face down. That way I can do that when I don't want to be disturbed.
You can set that up with Tasker pretty easily. I hadn't considered it before now but I just set mine up to go to vibrate when I flip it over.