BackboneMixin.js

define([
], function() {
  return {
    componentDidMount: function() {
      this._boundForceUpdate = this.forceUpdate.bind(this, null);
      this.getBackboneObject().on("all", this._boundForceUpdate, this);
    },
    componentWillUnmount: function() {
      this.getBackboneObject().off("all", this._boundForceUpdate);
    },
    getBackboneObject: function() {
      return this.props.collection || this.props.model;
    }
  };
});

Bootstrap.js

/** @jsx React.DOM */

define([
  "Backbone",
  "React",
  "ListComponent"
], function(React, ListComponent) {
  var ListItem = Backbone.Model.extend({});
  var ListItemCollection = Backbone.Collection.extend({
    model: ListItem
  });

  var listItemCollection = new ListItemCollection();

  React.renderComponent(
    <ListComponent collection={listItemCollection} />,
    document.body
  );

  listItemCollection.set([
    new ListItem(),
    new ListItem(),
    new ListItem()
  ]);
});

ListComponent.js

/** @jsx React.DOM */

define([
  "React",
  "BackboneMixin"
], function(React, BackboneMixin) {
  return React.createClass({
    mixins: [BackboneMixin],
    render: function() {
      var listItems = this.props.collection.map(function(model) {
        return (<li key={model.cid}>{model.cid}</li>);
      });

      return (
        <ul>
          {listItems}
        </ul>
      );
    }
  });
});