jQuery ≥ 1.7

With jQuery 1.7 onward the event API has been updated, .bind()/.unbind() are still available for backwards compatibility, but the preferred method is using the on()/off() functions. The below would now be,

$('#myimage').click(function() { return false; }); // Adds another click event
$('#myimage').off('click');
$('#myimage').on('click.mynamespace', function() { /* Do stuff */ });
$('#myimage').off('click.mynamespace');

jQuery < 1.7

In your example code you are simply adding another click event to the image, not overriding the previous one:

$('#myimage').click(function() { return false; }); // Adds another click event

Both click events will then get fired.

As people have said you can use unbind to remove all click events:

$('#myimage').unbind('click');

If you want to add a single event and then remove it (without removing any others that might have been added) then you can use event namespacing:

$('#myimage').bind('click.mynamespace', function() { /* Do stuff */ });

and to remove just your event:

$('#myimage').unbind('click.mynamespace');