error_reporting(E_ALL | E_STRICT);
define('MAGENTO_ROOT', getcwd());
$mageFilename = MAGENTO_ROOT . '/app/Mage.php';
require_once $mageFilename;
Mage::setIsDeveloperMode(true);
ini_set('display_errors', 1);
Mage::app();
$products = Mage::getModel("catalog/product")->getCollection();
$products->addAttributeToSelect('category_ids');
$products->addAttributeToFilter('status', 1);//optional for only enabled products
$products->addAttributeToFilter('visibility', 4);//optional for products only visible in catalog and search
$fp = fopen('exports.csv', 'w');
$csvHeader = array("sku", "category_ids","category_name");
fputcsv( $fp, $csvHeader,",");
$cat_name = array();
$cat_array = array();
$cat = Mage::getModel('catalog/category');
foreach ($products as $product)
{
$sku = $product->getSku();
$categoryIds = implode('|', $product->getCategoryIds());//change the category separator if needed
$cat_name = array();
$cat_array = $product->getCategoryIds();
for($k = 0; $k < count($cat_array); $k++)
{
$id = $cat_array[$k];
$cat->load($id);
$cat_name[] = $cat->getName();
}
$_cate_name = implode('|',$cat_name);
fputcsv($fp, array($sku, $categoryIds,$_cate_name), ",");
}
fclose($fp);

Admin
https://www.apps4rent.com
https://www.o365cloudexperts.com
https://www.clouddesktoponline.com

I am also interested in this feature. It would avoid some manual work later on :-)