As of jQuery 1.7 you should be using off to remove event handlers and on to add them, though you can still use the click shorthand.
$('#clickme').off('click').on('click', fireclick);
$('#clickme').off().on('click', fireclick);
Original answer:
If you want to replace all click handlers, call unbind first without a function argument. If you want to replace all event handlers, don’t specify the event type.
$('#clickme').unbind('click').click(fireclick);
$('#clickme').unbind().click(fireclick);