a little plugin for it.

(function($) {
    $.fn.hasScrollBar = function() {
        return this.get(0).scrollHeight > this.height();
    }
})(jQuery);

use it like this,

$('#my_div1').hasScrollBar(); // returns true if there's a `vertical` scrollbar, false otherwise..

tested working on Firefox, Chrome, IE6,7,8

but not working properly on body tag selector

demo

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Edit

I found out that when you have horizontal scrollbar that causes vertical scrollbar to appear, this function does not work….

I found out another solution… use clientHeight

return this.get(0).scrollHeight > this.get(0).clientHeight;