I had the same problem. Did a lot of googling with no help.
In my case it turned out I was testing the alert ringtone only for messages sent from one particular phone. That one message thread on my iphone had been set to "Do Not Disturb". (a new feature of IOS 8) It makes sense since I had been playing with some of those settings earlier in the day, but didn't realize that I'd left it that way.
You can find that setting by tapping on "details", at the top right of the screen, when looking at a particular message thread.
Another possibility is go to Settings > Sounds and
- Check the volume setting,
- Try turning off "Change With Buttons"
You can also check the more general "Do Not Disturb" settings in the control panel". If the Moon is highlighted that means "Do Not Disturb" is on. If needed, you can permanently fix that in settings > "Do Not Disturb"
Pete