Just for posterity, the current canonical list of testing that seems to absolutely require human beings' attention seems to be:

GUI/usability testing
security/penetration testing
performance testing

and many people think that adding some Exploratory Testing to your project is an excellent idea. (Note: Firefox does not like those links. You might need a different browser to view the pages or to get the .pdf.)
UPDATE: benizi helped fix the links, they should work now.