This is the classic Backbone Todos app, refactored to leverage CoffeeScript and Rails' Asset Pipeline, and backended by a Rails JSON API.
git clone git://github.com/dthtvwls/rails-backbone-todos.git
cd rails-backbone-todos/
bundle install
rake db:schema:load
rails server
open http://localhost:3000
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.