How can I capture the right-click event in JavaScript?

Use the oncontextmenu event.

Here’s an example:

<div oncontextmenu="javascript:alert('success!');return false;">
    Lorem Ipsum
</div>

And using event listeners (credit to rampion from a comment in 2011):

el.addEventListener('contextmenu', function(ev) {
    ev.preventDefault();
    alert('success!');
    return false;
}, false);

Don’t forget to return false, otherwise the standard context menu will still pop up.

If you are going to use a function you’ve written rather than javascript:alert("Success!"), remember to return false in BOTH the function AND the oncontextmenu attribute.