For the 2013 competition I created part of an app(it's not totally done yet) that allows you to look up who your state reps are based upon your current gps coordinates.
To expand upon this, I was going to create a redit like upvote and commenting system, but I ran out of patience, and then time.
This was my first excercise combining jQuery Mobile with Backbone.js built on top of a readbeanphp beancan json-rpc backend. After really digging into the project and discovering the recomended way of routing with jQm and backbone wasn't going to do what I wanted, and I ended up wasting a lot of time writing my own router. It's still has some bugs, but works pretty well considering the time I've invested and the time crunch I was under. I hope to get the code up on github soon for others to enjoy.
In the end, I really enjoyed using backbone, and it was impressive how little php I had to write, and how fast it makes jQm.