I'd really like to resurrect this thread to see if we can get further input as to what you think makes a great photo essay. Feel free to add links to examples.
Basic criteria for an essay (words or pictures), as found in "Creative Writing 101":
It needs to have a beginning, a middle and an end (in other words, a narrative flow).
Write about [photograph] what you know.
Use the simplest possible words [images] which are adequate for your subject.
Write [make images] using your own voice.
With particular reference to photos, a further factor is that you must unhesitatingly discard an individual image, no matter how brilliant you think it is, if it does not contribute to the essay as a whole. Conversely, you must be ready to re-shoot again and again if necessary to fill in holes in the narrative.
As others have remarked, current forms of image presentation are not very essay-friendly. If I try to think of examples, the name W. Eugene Smith comes to mind, with his "Life" essays, for example "A Spanish Village", and his book-length essay "Minamata".
Regards,
David