React + Webpack + Rails

.babelrc

{
  "presets": ["es2015", "react"]
}

application.js

// This is a manifest file that'll be compiled into application.js, which will include all the files
// listed below.
//
// Any JavaScript/Coffee file within this directory, lib/assets/javascripts, vendor/assets/javascripts,
// or any plugin's vendor/assets/javascripts directory can be referenced here using a relative path.
//
// It's not advisable to add code directly here, but if you do, it'll appear at the bottom of the
// compiled file.
//
// Read Sprockets README (https://github.com/rails/sprockets#sprockets-directives) for details
// about supported directives.
//
//= require jquery
//= require jquery_ujs

//= require_tree .

index.html.erb

<div id="react"></div>

package.json

{
  "dependencies": {
    "babel-core": "^6.10.4",
    "babel-loader": "^6.2.4",
    "babel-preset-es2015": "^6.9.0",
    "babel-preset-react": "^6.11.1",
    "events": "^1.1.1",
    "flux": "^2.1.1",
    "react": "^15.2.1",
    "react-dom": "^15.2.1",
    "react-router": "^2.6.0",
    "webpack": "^1.13.1"
  }
}

webpack.config.js

module.exports = {
  entry: "./app/assets/react/main.jsx",
  output: {
      path: __dirname + "/app/assets/javascripts",
      filename: "bundle.js"
  },
  resolve: {
    extensions: ['', '.js', '.jsx']
  },
  module: {
    loaders: [
      { test: /\.jsx$/, loader: 'babel-loader' }
    ]
  }
}