How to capture the browser window close event?

For a cross-browser solution (tested in Chrome 21, IE9, FF15), consider using the following code, which is a slightly tweaked version of Slaks' code:

var inFormOrLink;
$('a').live('click', function() { inFormOrLink = true; });
$('form').bind('submit', function() { inFormOrLink = true; });

$(window).bind('beforeunload', function(eventObject) {
    var returnValue = undefined;
    if (! inFormOrLink) {
        returnValue = "Do you really want to close?";
    }
    eventObject.returnValue = returnValue;
    return returnValue;
}); 

Note that since Firefox 4, the message "Do you really want to close?" is not displayed. FF just displays a generic message. See note in https://developer.mozilla.org/en-US/docs/DOM/window.onbeforeunload

The beforeunload event fires whenever the user leaves your page for any reason.

For example, it will be fired if the user submits a form, clicks a link, closes the window (or tab), or goes to a new page using the address bar, search box, or a bookmark.

You could exclude form submissions and hyperlinks (except from other frames) with the following code:

var inFormOrLink;
$('a').on('click', function() { inFormOrLink = true; });
$('form').on('submit', function() { inFormOrLink = true; });

$(window).on("beforeunload", function() { 
    return inFormOrLink ? "Do you really want to close?" : null; 
})

For jQuery versions older than 1.7, try this:

var inFormOrLink;
$('a').live('click', function() { inFormOrLink = true; });
$('form').bind('submit', function() { inFormOrLink = true; });

$(window).bind("beforeunload", function() { 
    return inFormOrLink ? "Do you really want to close?" : null; 
})

The live method doesn't work with the submit event, so if you add a new form, you'll need to bind the handler to it as well.

Note that if a different event handler cancels the submit or navigation, you will lose the confirmation prompt if the window is actually closed later. You could fix that by recording the time in the submit and click events, and checking if the beforeunload happens more than a couple of seconds later.

Maybe just unbind the beforeunload event handler within the form's submit event handler:

jQuery('form').submit(function() {
    jQuery(window).unbind("beforeunload");
    ...
});