By default, if you enter attribute options in the back end, you can't add an empty option to the attribute. Maybe these empty options were added via a custom script. Here is the custom script that helps you to remove the empty options of the attributes

1.Create store_root/shell/empty.php file with code snippet:

<?php
require_once 'abstract.php';
class Empty_Attribute_Remover extends Mage_Shell_Abstract
{
    public function run()
    {
        $attribute                  = Mage::getModel('catalog/resource_eav_attribute')
          ->loadByCode(Mage_Catalog_Model_Product::ENTITY, 'some_attribute_code');

        $optionCollection = Mage::getResourceModel('eav/entity_attribute_option_collection')
            ->setAttributeFilter($attribute->getAttributeId())
            ->setPositionOrder('desc', true)
            ->load();
        foreach($optionCollection as $option){
            //remove if options value is empty
            if ($option->getValue()=='') {
                $option->delete();
            }
        }
    }
}

$shell = new Empty_Attribute_Remover();
$shell->run();

2.Run this PHP script to remove empty options of the attribute with some_attribute_code:

php -f shell/empty.php