Edit in JSFiddle

Result
JavaScript
CSS
HTML

$('iframe[src*="youtube.com"]').each(function () {
    var RemoveRelated = $(this).attr('src');
    if (jQuery.inArray('rel=0',RemoveRelated) == -1) {
        $(this).attr('src', RemoveRelated + '?rel=0');
    }
});

<iframe width="560" height="315" src="http://www.youtube.com/embed/g31LLr1_KFk" frameborder="0" allowfullscreen></iframe>