router.js

Ember.Route.reopen({
  activate: function() {
    var cssClass = this.toCssClass();
    // you probably don't need the application class
    // to be added to the body
    if (cssClass !== 'application') {
      Ember.$('body').addClass(cssClass);
    }
  },
  deactivate: function() {
    Ember.$('body').removeClass(this.toCssClass());
  },
  toCssClass: function() {
    return this.routeName.replace(/\./g, '-').dasherize();
  }
});