Organisation relationship search
You can use this SQL if you have access to the database directly. Replace the "5" with the actual id of the relationship type you're interested in. If you don't know the id you can see it if you go to admin - customize - relationship types and hover over the view link then you'll see the id in the url in the browser status bar.

select c.display_name from civicrm_contact c left join civicrm_relationship r on (r.contact_id_a=c.id AND r.relationship_type_id=5) where c.contact_type='Organization' and r.id IS NULL;

Depending on which direction you've defined the relationship you may need to replace contact_id_a with contact_id_b above.

I think there's a bug in the CiviReport - Contact Reports - Relationship Report otherwise you might be able to do it from there, setting contact type A to be Organization and relationship to be "Is Empty", but it doesn't seem to recognize the latter properly.