It is possible, if you don't use anonymous callbacks:

var $elt = $(...);

function clickHandler1(event){...}
function clickHandler2(event){...}

// bind both
$elt.click(clickHandler1);
$elt.click(clickHandler2);

// unbind just the first
$elt.unbind('click', clickHandler1);

A wild Demo appeared!

See also: .unbind() docs.

Actually, you can do it using anonymous callbacks via event namespacing:

$elt.bind('click.handler1', function(event) {
    alert('click handler 1');
});

$elt.unbind('click.handler1');

See modified demo here.

And here for more information.

This was added in jQuery 1.4.3, which actually came out more than 4 months before the question was asked.

This post is ages old, so I thought I'd chime in with how this is done today (2019).

Most of the old answers above, including the accepted answer (which was correct when it was written), use the unbind method which has been deprecated since jQuery v.3.0.

As of jQuery 3.0, .unbind() has been deprecated. It was superseded by the .off() method since jQuery 1.7, so its use was already discouraged.

Source

Here's how to do it with the .off() method:

var foo = function() {
  // Code to handle some kind of event
};

// ... Now foo will be called when paragraphs are clicked ...
$( "body" ).on( "click", "p", foo );

// ... Foo will no longer be called.
$( "body" ).off( "click", "p", foo );

Source

This will work for all event handlers implemented with the .on() method and it works for undelegated event handlers as well. Simply replace "body" with your element selector and remove the second parameter of the .off() method ("p" in the example above).