Capture key press without placing an input element on the page?

For modern JS, use event.key!

document.addEventListener("keypress", function onPress(event) {
    if (event.key === "z" && event.ctrlKey) {
        // Do something awesome
    }
});

NOTE: The old properties (.keyCode and .which) are Deprecated.

Mozilla Docs

Supported Browsers

For non-printable keys such as arrow keys and shortcut keys such as Ctrl-z, Ctrl-x, Ctrl-c that may trigger some action in the browser (for instance, inside editable documents or elements), you may not get a keypress event in all browsers. For this reason you have to use keydown instead, if you're interested in suppressing the browser's default action. If not, keyup will do just as well.

Attaching a keydown event to document works in all the major browsers:

document.onkeydown = function(evt) {
    evt = evt || window.event;
    if (evt.ctrlKey && evt.keyCode == 90) {
        alert("Ctrl-Z");
    }
};

For a complete reference, I strongly recommend Jan Wolter's article on JavaScript key handling.

jQuery also has an excellent implementation that's incredibly easy to use. Here's how you could implement this functionality across browsers:

$(document).keypress(function(e){
    var checkWebkitandIE=(e.which==26 ? 1 : 0);
    var checkMoz=(e.which==122 && e.ctrlKey ? 1 : 0);

    if (checkWebkitandIE || checkMoz) $("body").append("<p>ctrl+z detected!</p>");
});

Tested in IE7,Firefox 3.6.3 & Chrome 4.1.249.1064

Another way of doing this is to use the keydown event and track the event.keyCode. However, since jQuery normalizes keyCode and charCode using event.which, their spec recommends using event.which in a variety of situations:

$(document).keydown(function(e){
if (e.keyCode==90 && e.ctrlKey)
    $("body").append("<p>ctrl+z detected!</p>");
});