I wrote this one for our local high school:
http://m.apexcougarclub.org
It isn't a true "App" per se as it isn't a native IOS or Android installed application. Instead it is a Mobile Web App written in Ruby on Rails and jQuery Mobile. It will run in any modern browser but looks best on a phone or tablet. It even installs a launch icon on your device if you allow it to.
Mobile Web Apps (and there are number of platforms to build them with) have pros and cons. They are very quick to get up and running and easy to iterate on quickly. You lose some of the native functionality of a mobile platform but for a lot of use cases, that is no big deal.
I had never written anything in Ruby before I did this - it is pretty easy to pick up.
If your App idea doesn't involve a lot of data or screens, you may be able to prototype the whole thing with jQuery Mobile. This book walks you through the process:
http://amzn.com/1449397654