Here's how I'd do it:
Code:
$result = mysql_query( "SELECT category_id, category_name FROM np_categories ORDER BY category_name ASC" );
while( $row = mysql_fetch_array( $result ) )
{
$category_id = $row[0];
$name = $row[1];
$data = mysql_fetch_array( mysql_query( "SELECT COUNT(*) FROM np_articles WHERE article_category_id = $category_id" ) );
$num_articles = $data[0];
print( "<li> $name ($num_articles)</li>\n" );
}