Hide Attribute if Attribute Value is Empty Space in Magento

The code in tabs.phtml looks like this:

<ul class="product-tabs">
    <?php foreach ($this->getTabs() as $_index => $_tab): ?>
        <?php if($this->getChildHtml($_tab['alias'])): ?>
            <li id="product_tabs_<?php echo $_tab['alias'] ?>" class="<?php echo !$_index?' active first':(($_index==count($this->getTabs())-1)?' last':'')?>"><a href="#"><?php echo $_tab['title']?></a></li>
        <?php endif; ?>
    <?php endforeach; ?>
</ul>
<?php foreach ($this->getTabs() as $_index => $_tab): ?>
    <?php if($this->getChildHtml($_tab['alias'])): ?>
        <div class="product-tabs-content" id="product_tabs_<?php echo $_tab['alias'] ?>_contents"><?php echo $this->getChildHtml($_tab['alias']) ?></div>
    <?php endif; ?>
<?php endforeach; ?>

So if a tab content is empty then the tab is not shown.
Either you have a different code, or your tab content is not empty. It may contain something like <div></div> or something like that.
In this case you can change the if statement to remove your tags.
Maybe something like this:

<ul class="product-tabs">
    <?php foreach ($this->getTabs() as $_index => $_tab): ?>
        <?php if(trim(strip_tags($this->getChildHtml($_tab['alias'])))): ?>
            <li id="product_tabs_<?php echo $_tab['alias'] ?>" class="<?php echo !$_index?' active first':(($_index==count($this->getTabs())-1)?' last':'')?>"><a href="#"><?php echo $_tab['title']?></a></li>
        <?php endif; ?>
    <?php endforeach; ?>
</ul>
<?php foreach ($this->getTabs() as $_index => $_tab): ?>
    <?php if(trim(strip_tags($this->getChildHtml($_tab['alias'])))): ?>
        <div class="product-tabs-content" id="product_tabs_<?php echo $_tab['alias'] ?>_contents"><?php echo $this->getChildHtml($_tab['alias']) ?></div>
    <?php endif; ?>
<?php endforeach; ?>

A quick fix:

In app/[mypackage]/[mytheme]/template/catalog/product/view/attributes.phtml (or copy this file in your theme from base or default custom theme):

<?php foreach ($_additional as $_data):
// Add these 2 lines
$_test_data_value = trim($_data['value']);
if ((empty($_test_data_value) || in_array($_test_data_value, array(Mage::helper('catalog')->__('N/A'), Mage::helper('catalog')->__('No'))))) continue;?>

Below is not necessary to achieve what you've asked:

Those attributes are still loaded. To optimize this (if you have a big number of attributes in attributes sets) do:

public function getAdditionalData(array $excludeAttr = array())
{
    $data = array();
    $product = $this->getProduct();
    $attributes = $product->getAttributes();
    foreach ($attributes as $attribute) {
//            if ($attribute->getIsVisibleOnFront() && $attribute->getIsUserDefined() && !in_array($attribute->getAttributeCode(), $excludeAttr)) {
        if ($attribute->getIsVisibleOnFront() && !in_array($attribute->getAttributeCode(), $excludeAttr)) {

            // Fix:
            //$value = $attribute->getFrontend()->getValue($product);

            if (!$product->hasData($attribute->getAttributeCode())) {
                $value = Mage::helper('catalog')->__('N/A');
            } 
            // Fix:
            elseif ((string) ($value = $attribute->getFrontend()->getValue($product)) == '') {
                $value = Mage::helper('catalog')->__('No');
            } elseif ($attribute->getFrontendInput() == 'price' && is_string($value)) {
                $value = Mage::app()->getStore()->convertPrice($value, true);
            }

            if (is_string($value) && strlen($value)) {
                $data[$attribute->getAttributeCode()] = array(
                    'label' => $attribute->getStoreLabel(),
                    'value' => $value,
                    'code'  => $attribute->getAttributeCode()
                );
            }
        }
    }
    return $data;
}

Note the two // Fix: comments.

This modified function is from Mage_Catalog_Block_Product_View_Attributes. You need to copy the function above in your block class from your module. Your block class rewrites the core block class. Applying this will improve considerably product view page load on frontend.

If you don't know how to create a custom module in local dir than search a tutorial on how to create a Magento module and how to rewrite a core block class. Or try http://www.magentocommerce.com/magento-connect/ultimate-module-creator.html.