For about six months, my iPhone 6s phone would not ring but I found the answer. The key was this thread on the Apple discussion boards. Even though this discusses the model 5s, it worked. Thanks to the semi-anonymous poster pidon for noticing this.
Overview
There are many places to adjust various aspects of the iPhone’s sounds. A good start is in Settings/Do Not Disturb. I’ll run through the complete list after I describe what finally worked for me. Interestingly, this is a quick hardware fix, not part of the Settings menu system.
A Small Switch
In my case, there were no sounds playing. No tweet when I tweeted. No swoosh when I sent an e-mail. No … well, to avoid the scatological, I’ll just say there were many sounds that did not work. Warning: you might like that setting. Benefit: here’s an easy way to turn off all the sounds at once.
For me, the key was my Otter iPhone case that may have caused the problem. When I installed it, I also accidentally flipped the ring/silent switch. However, this problem is not exclusive to Otter cases. It’s easy to accidentally flip this switch and not even realize what’s happened.
The switch in question is identified on page 9 of Apple’s instructions:
Here’s what to do. First, locate the cover flap next to the volume control buttons:
Open the flap. If you see this you’ve identified the source of the trouble. Look for the color orange:
Flip the switch so it looks like this:
Call your phone from another phone. If you still don’t get a ring, read on.
Software Issues: Do Not Disturb
Far and away the most likely culprit is the Do Not Disturb option in Settings. And one of the easiest things to overlook is the Allow Calls From feature. Not only can you allow calls from Everyone, No One, or Favorites, you can also select a contact group – or even All Contacts. I just set mine to Everyone. You may be fussier. But I don’t get many calls, so this is easy. Caller ID is good enough for me.
Software Issues: Other Suspects
For better or worse, there are several other Settings items that can affect how the phone function notifies you of various actions. Settings/Notifications/Phone:
And, of course, there is the laundry list of items under Settings/Sounds. Scroll to the bottom of the list to find Keyboard Clicks and Lock Sound.
Oddly enough Voice Dialing is part of the Touch ID & Passcode menu. Most likely the reason is that you must enter your passcode to access this menu.
Finally, there is the Homer Simpson D’OH item, Settings/Phone. While it doesn’t look like any of these options will actually turn off the phone’s ringer, if nothing else has worked, try this.
One or two people on the Apple discussion board suggested a soft reset. Hold the sleep/wake and home buttons for at least ten seconds until you see the Apple logo:
iPhone 7 and newer: hold the sleep/wake and volume down buttons.
Otter Details
My Otter case is an iPhone 6/6s Defender Series Case ($49.95 from manufacturer, less elsewhere). Click here to see all Otter cases for Apple products. I am a satisfied Otter customer who paid the retail price for my Otterbox.
Conclusion
I doubt very much that this list is comprehensive. But I hope it’s a good start.