This is the classic Backbone Todos app, refactored to leverage CoffeeScript and Rails' Asset Pipeline, and backended by a Rails JSON API.
If you don't already know this dance:
git clone git://github.com/dthtvwls/rails-backbone-todos.git
For a really fun time
Check http://localhost:3000/todos.json while you use the Backbone app to see the data updating. All communication between Backbone and Rails is over the API; front and back ends are completely decoupled.