I just figured out a fairly simple way to get alerts when my doorbell is rung. I have a wired 24v doorbell.
I believe many others work the same way as mine:
Pushing the doorbell outside triggers a magnetic coil inside that fires a pin to hit the bell.
I figured if it's using magnetic power, then it might work with a z-wave door/window sensor. I took a z-wave door/window sensor and taped it right by the doorbell's magnetic coil. It works flawlessly. The doorbell ringing affects that coil enough to make the z-wave sensor think that it switched from open to closed.
I don't quite have the know-how to create a smartapp for this, so I just called it a door sensor and set up an alert for when the door sensor opens. So when someone rings the doorbell I get this message, "Doorbell is open". Ideally I wouldn't have to call it a door sensor and the message could say, "Doorbell was rung", but I'm sure someone smarter than I am can figure that out.
The other downside is that as you can see in the picture, the enclosure doesn't fit all the way on anymore. It's up high in a hallway, so no one actually notices it, but I assume someone else might know a way to take the z-wave sensor apart to make it small enough to fit inside cleanly. I also would assume that one of those recessed door sensors would fit inside the enclosure fine.
Some reasons why I wanted alerts for my doorbell:
1) When I'm not on the main floor, it is pretty hard to hear the doorbell, especially if there is music or a TV on.
2) We've had several break-ins in my neighborhood. The thieves would knock and ring the doorbell first to make sure no one was home before entering. If someone answered the door, they would just pretend to be selling something. Now if we're not home, my wife and I get an alert and can very quickly look at our front door camera and see who it is. If it looks like they are up to no good, we could either flash some lights in the house on and off, or worst case scenario, call the police.