Your bind, unbind methods are misplaced.
$('#button').on('click', Button_Click);
function Button_Click(){
$(this).after('<span> click is active</span>');
$('span').fadeOut(1000);
}
$('#toggle').toggle(
function(){
$(this).text('rebind').removeClass('unbind').addClass('rebind');
$('#button').unbind('click');
},
function(){
$(this).text('unbind').addClass('unbind').removeClass('rebind');
$('#button').bind('click',Button_Click);
}
);
http://jsfiddle.net/FtATg/
Also as of jQuery 1.7, the .on() and .off() methods are preferred to attach and remove event handlers on elements.