contenteditable change events

Here is a more efficient version which uses on for all contenteditables. It's based off the top answers here.

$('body').on('focus', '[contenteditable]', function() {
    const $this = $(this);
    $this.data('before', $this.html());
}).on('blur keyup paste input', '[contenteditable]', function() {
    const $this = $(this);
    if ($this.data('before') !== $this.html()) {
        $this.data('before', $this.html());
        $this.trigger('change');
    }
});

The project is here: https://github.com/balupton/html5edit

2022 update

As pointed out in the comments, this doesn't answer the question asked, which wanted the equivalent of the change event rather than the input event. However, I'll leave it here as is.

Original answer

I'd suggest attaching listeners to key events fired by the editable element, though you need to be aware that keydown and keypress events are fired before the content itself is changed. This won't cover every possible means of changing the content: the user can also use cut, copy and paste from the Edit or context browser menus, so you may want to handle the cut copy and paste events too. Also, the user can drop text or other content, so there are more events there (mouseup, for example). You may want to poll the element's contents as a fallback.

UPDATE 29 October 2014

The HTML5 input event is the answer in the long term. At the time of writing, it is supported for contenteditable elements in current Mozilla (from Firefox 14) and WebKit/Blink browsers, but not IE.

Demo:

document.getElementById("editor").addEventListener("input", function() {
    console.log("input event fired");
}, false);

<div contenteditable="true" id="editor">Please type something in here</div>

Demo: http://jsfiddle.net/ch6yn/2691/