You don t need to use addFieldToFilter.

now the solution:
attributes name is known as code in magento, you just need to use the code below to get all of the products which have a specific attribute as an array

$prodsArray=Mage::getModel( catalog/product )->getCollection()
                                  ->addAttributeToFilter( custom_attribute_code )
                                  ->getItems();

you can also specify certain conditions for attribute s value in addAttributeToFilter in the second parameter of addAttributeToFilter.

you can find this method in this file (for further study):

app/code/core/Mage/Eav/Model/Entity/Collection/Abstract.php

I see you already found a solution, but there is also this option:

$collection->addFieldToFilter( parent_item_id , array( null  => true));

But if you want to use "NULL" => false, which DOESN T WORK. (and I noticed you can use elements such as "in", "nin", "eq", "neq", "gt"), you can do this:

$collection->addFieldToFilter( parent_item_id , array( neq  =>  NULL  ));

Hope this is still helpful...

This works for NOT NULL filters

$collection->addFieldToFilter( parent_item_id , array( notnull  => true));

Filtering a product collection by null/empty attributes has two possible solutions. Magento uses an INNER JOIN to grab the values of the attributes to filter. BUT if the product attribute is not assigned a value the join will fail, as a database table / relationship is missing.

Solution #1: Use addAttributeToFilter() and change the join type from "inner" (the default) to "left":

$collection = Mage::getModel( catalog/product )->getCollection();
$collection->addAttributeToFilter( custom_attribute , array( ... condition options ..),  left );

Solution #2: Make sure your custom attribute has a default value. Magento is conservative in this regard. Magento will only create the relationship between an attribute and a product if a value is given for the attribute. So in the absence of user-specified value or a default value the attribute will not be accessible for filtering a product even if the attribute appears in the product detail view under the admin panel.

Because the question does not match exactly the title of the question and I found the them multiple times by searching for a condition like: special VALUE OR NULL

If you want to filter a collection matching a VALUE OR NULL, then you can use:

$collection->addFieldToFilter( <attribute> , array(
  array( eq  =>  <value> ),
  array( null  => true)
));