How do I enable continuous deployment of Node.js applications to Amazon EC2?

That auto-deploy mechanism is implemented with Git Hooks. The most likely hook used is post-update.

It's a simple bash script that is executed on a git push; put one in a git repository on your EC2 server including the code to re-run NPM (if needed) and restart your code.

That's should do it. :)

Use roco - deployment solution inspired by capistrano, working great with express/railwayjs + git + upstart. If you have another env feel free to customize it using Roco.coffee

It also can be simply configured with post-update hook to work exacty as in heroku and joyent.

Here is tiny tutorial for this tool: http://node-js.ru/4-deploy-with-roco

Check out AWS Elastic Beanstalk

It lets you deploy your application to an amazon ec2 instance by running:

git aws.push --environment testing
// or
git aws.push --environment production

The documentation page contains a lot of quality information to get your started!