I tried using Browserify with some React.js code. Turns out I needed Reactify to get it working.
https://github.com/jesseskinner/react-browserify-demo

For further reading, check out:
React.js - http://facebook.github.io/react/
React Tutorial - http://facebook.github.io/react/docs/tutorial.html
Browserify - http://browserify.org/
Reactify - https://github.com/andreypopp/reactify