Option 1: Electron (formerly atom-shell)
This is the shell that GitHub's Atom and Microsoft's Code editors use. It’s very similar to node-webkit, though it will run the script first, and you have to create a view/window for the user. There are some other minor differences, but it's worth looking at.
Option 2: NW.js formerly node-webkit
The gist is that it basically extends the JavaScript engine for you to write a web-based application supporting Node.js' extended object model, and modules... you then package your package.json start.html modules and JavaScript files into a ZIP file (with the .nw extension) and run it with nw(.exe) .. there are Windows, Mac and Linux builds available.
Option 3: Neutralinojs Github
Neutralinojs is a lightweight and portable desktop application development framework. It lets you develop lightweight cross-platform desktop applications using JavaScript, HTML and CSS. You can extend Neutralinojs with any programming language (via extensions IPC) and use Neutralinojs as a part of any source file (via child processes IPC).
Option 4: MacGapNode (OS X only)
MacGap with Node.js integration (it seems to be getting stale)
Option 5: Tauri Github
Tauri is a toolkit that helps developers make applications for the major desktop platforms - using virtually any frontend framework in existence. The core is built with Rust and the CLI leverages Node.js making Tauri a genuinely polyglot approach to creating and maintaining great apps.
Aside: Services...
I can't speak for OS X on this as a .App, but it could well be possible to create a background service install in Node.js and a link to a "local" site on the desktop. Most browsers have an option to not show all the features (I know Firefox in particular does).
I know your question is to OS X in particular, but in Windows you can use NSSM to run anything as a service, and I have used it for Node.js-based services in Windows. I think some of the other options above are better depending on your needs though.
Removed:
This answer is copied for multiple questions, and these references are mostly for updating convenience.