Imperial Japan (from the Meiji Restoration until Surrender in 1945 to American Forces) would be a Theocracy as the Emperor was considered a living deity (prior to Meiji Restoration, the Emperor had very little political power compared to the Shogun. After the Military Occupation by the United States it is the Prime Minister of the Diet (some Japanese will often refer to the Military Governor General MacAurthor as "the last shogun" as he his role was basically that of the Shogun). Part of the terms of surrender were the Emperor's renunciation as a living diety (though the royal family still claims divine ancestry).
Saudi Arabia is a Theocracy as they officially view the Quoran as the Constitution of the Nation and use Shia Law, which uses Islamic Law derived from the Quoran and Hadiths as source of law. Other Middle East states may be Theocratic in general as well (Israel is definitely not as there is a difference between one who is ethnically Jewish and one who is Religiously Jewish. Israel is an ethnic Jewish State, but it's laws are grounded in Secular Common Law derived from English Law).
Vatican City, by virtue of the fact that it's head of state and government is the Pope. It's important to note that the distinction between the Head of State and Head of Government is important (they need not be invested in the same position, though some states do have a single person with both roles, the U.S. being the best known one).
Typically Theocracies are those in which a cleric or other official holds the role of Head of Government (and typically Head of State), hence why Britain and Japan in the present day aren't theocracies despite both having Monarchs as spiritual leaders for their nation's faithful (because much of government authority is vested in secular officials and both are not Heads of Government) while Saudi Arabia is a Theocracy (The King rules by divine right and is both the Head of Government and Head of State).
One could argue North Korea as technically Kim Il Sung is the Head of State and Government despite his present inability to make important national leader decisions on account of having a chronic case of being dead (no really... I had to hold back from saying "He's dead, Jung" because that was too goofy) His "successors" (His son Kim Jong Il and grandson Kim Jong Un) are place holders for him until presumably the Zombie Apocalypse happens, and it functions more as a regent than actual ruler... or like that time where Dick Cheney was Acting President for a couple of hours because George Bush was getting routine surgery and was out like a light... only Sung's been out like a light for a lot longer. I'm not well versed on the spiritual nature of the North Korean people, so I can't comment much on why the NK government holds this position, but if I had a dime for every time I saw the NK government make a claim that operates on a logic that does not exist anywhere remotely close to this planet, I'd be a very rich man.