I'd go with a hybrid of RaYell's and phoenix's solution, adding jQuery's namespacing to the mix:
$('#addlink').bind('click.killlink',function(event){
    event.preventDefault();
    // You can do any additional onClick behavior here
});
To unbind this event, as well as any other related events (of any type) that you group with the .killink namespace, you'd run this:
$('#addlink').unbind('.killlink');
As phoenix pointed out, using return false will prevent the event from bubbling up. preventDefault() has the added benefit of being extremely explicit (unlike return false, which can mean many different things depending on the context).