: I almost used "Theocracy", but I usually assoicate those forms of government with priests. Maybe I'm forgetting another word.

I think the best term to use would be autocracy - absolute power residing in the hands of a single sovereign. Sauron himself could be described as an autarch, a tyrant, or even a despot, all of which mean pretty much the same thing.

One problem with trying to categorize this type of 'government' is that we have no equivalent in our own history. The closest approximation would probably be the ancient Egyptian Pharaohs. Technically, the Pharaoh was a living god subject to no earthly authority. In reality, with the exception of the reigns of certain warrior-kings (such as Seti I and Ramesses II) during which the military was the dominant power, the country of Egypt was controlled by the various priesthoods of the major gods.

Sauron's 'empire' was an amalgamation of several governmental forms. He was a military dictator, high-priest of his own state religion, an absolute monarch, and a living god. Obviously he had generals (or captains) who served under him and commanded his armies, and in all likelihood he probably also had a priesthood which performed religious ceremonies, collected taxes and offerings, etc.

Although Tolkien does not go into great detail, Sauron was running an empire, and that empire would have the same needs as other empires - soldiers to fight its wars; farmers to supply food; slaves to supply labor; money to finance expenses; priests, administrators, diplomats, spies, informants, etc. Yet, I find it highly unlikely that the Nazgul could have fulfilled many of these roles. For one thing, their 'people skills' were rather weak, making them unsuitable for most positions. Indeed, they seem to have been reserved for certain 'delicate' operations - ones which Sauron could trust to no one else. Also, had they been an integral part of Sauron's government, their absence during the Hunt for the Ring should have caused major disruptions in daily activities in both Mordor and Southern Mirkwood. It would seem to me that individuals such as the Mouth of Sauron and the Lieutenant of Morgul (and perhaps dozens of other leaders who are nowhere named) were responsible for the more mundane aspects of empire.

Regarding the hierarchy of Mordor, I would assume that the Nazgul occupied a unique position as Sauron's most trusted servants. The Lord of the Nazgul and Khamul seem to have had specific duties, but they are noted as being exceptional - the Witch-king in particular being said to have retained much of his will even after becoming a wraith.

After the Nazgul, the next most important figure was probably the Mouth of Sauron, being both the chief herald of his master and the ranking officer of the Barad-dur. Next would probably come the High Priest of Sauron (if such an individual existed), followed by the wardens (or lieutenants) of the key military sites - Minas Morgul, The Morannon, The Isenmouthe, Dol Guldur, Durthang, etc. After that, there would be lesser military leaders, priests, foreign dignitaries, kings and princes of allied (or subject) nations, sons of kings living as hostages in Mordor - all the way down to the common slave.