I know that there are many similar questions posted, but none of them refers to an HTML/javascript app where the user can access the code.
I have a private REST API written in nodejs. It is private because its only purpose is to server my HTML5 clients apps (Chrome app and Adobe Air app). So an API key is not a good solution since any user can see the javascript code.
I want to avoid bots creating accounts on my server and consuming my resources.
Is there any way to acomplish this?
An API key is a decent solution especially if you require constraints on the API key's request origin; consider that you should only accept an API key if the originating web request comes from an authorized source, such as your private domain. If a web request comes from an unauthorized domain, you could simply deny processing the request.
You can improve the security of this mechanism by utilizing a specialized encoding scheme, such as a hash-based message authentication code (HMAC). The following resource explains this mechanism clearly:
http://cloud.dzone.com/news/using-api-keys-effectively
What you want to do is employ mutually-authenticated SSL, so that your server will only accept incoming connections from your app and your app will only communicate with your server.
Here's the high-level approach. Create a self-signed server SSL certificate and deploy on your web server. If you're using Android, you can use the keytool included with the Android SDK for this purpose; if you're using another app platform, similar tools exist for them as well. Then create a self-signed client and deploy that within your application in a custom keystore included in your application as a resource (keytool will generate this as well). Configure the server to require client-side SSL authentication and to only accept the client certificate you generated. Configure the client to use that client-side certificate to identify itself and only accept the one server-side certificate you installed on your server for that part of it.
If someone/something other than your app attempts to connect to your server, the SSL connection will not be created, as the server will reject incoming SSL connections that do not present the client certificate that you have included in your app.
A step-by-step for this is a much longer answer than is warranted here. I would suggest doing this in stages as there are resources on the web about how to deal with self-signed SSL certificate in Android (I'm not as familiar with how to do this on other mobile platforms), both server and client side. There is also a complete walk-through in my book, Application Security for the Android Platform, published by O'Reilly.