Separating Head of State from Head of Government
There are not many countries in the world which combine the posts of head of government and head of state. One of the few that do, however, stands out for being the world's sole economic and military superpower (at least for now): the United States of America.
The American republic has one man (no woman has held that post to date, though she may emerge in 2008) who is its commander-in-chief. The President does not derive his authority from any other person.
Most other countries opt to separate the roles of head of government and head of state. Many go for a constitutional monarchy, under which the King or Queen is theoretically the most powerful person in the country, but delegates most of his or her power to an elected Prime Minister.
Others will instead choose the more egalitarian method of electing separate heads of government and heads of state. A few republics, such as India and Singapore, have gone this route.
There are exceptions, of course. Japan's monarch, the Emperor, has no actual constitutional position, so some have suggested that he could actually be done away with without the amendment of any laws. China had a somewhat similar position in the early 20th century, when Sun Yat Sen deposed the Emperor, but permitted him to remain in the Forbidden Palace, without any actual legal standing.
Thailand's monarch theoretically is subject to the Constitution, but is so revered by his people that he could probably have the Constitution rewritten at will. And a few countries, mainly Middle Eastern ones like Saudi Arabia and Jordan, but also countries like Brunei, still maintain monarchs with near-unfettered power.
With the republics, some oddly choose to make the head of state less than a full figurehead. France is one obvious example; its President wields so much power, that at times he can actually stymie the policies of the Prime Minister.
I think there is a reason that so many countries have chosen to separate the roles of head of government and head of state. Despite the added costs of providing an extravagant lifestyle for more people (such criticism is especially common in constitutional monarchies like the United Kingdom, but also in a few republics like France), there are obvious benefits to such an arrangement.
The circumstantial evidence alone is not encouraging for those who prefer a combination of the roles. Only America has been a shining success. Countries which have followed its model almost to a tee, such as the Philippines and many Latin American republics are, simply put, basket cases.
Correlation, of course, is not causation. What evidence, then, is there for the hypothesis that making the same person act as both head of government and of state is a bad decision?
I think one of the first and most apparent problems is that such an arrangement conflates the state and government. It is possible to criticise the government without criticising the state, and yet if you criticise your head of government, it will look like you are criticising your head of state.
This has been very common in countries like the United States, where those who criticise the President are accused of criticising the country. Such allegations would be almost impossible to make in Britain, where all we have are Her Majesty's Government and Her Majesty's Loyal Opposition.
(Government officials have apparently been able to make such allegations stick in constitutional monarchies such as Malaysia, however. One opposition lawmaker who criticised the King's speech from the throne at the opening of Parliament was accused of being disloyal to the King, even though the speech is written by the Prime Minister. Such a practice should probably be done away with, although it operates just fine in other Westminster democracies such as the UK.)
I do not think that this is the main reason for the failure of states that combine their heads of government and state. I think that the main reason may be that the power goes to the head of the leader. When you are the most powerful person in the land, both in name and in reality, it's a tad easy to get carried away with the notion that you can do anything you like.
The result is plain to see. The Philippines has had to grapple with two dictators who ran the nation into the ground, and there is grumbling that even the present President is corrupt. Zimbabwe has had its President, Robert Mugabe, turn the country into his personal fiefdom. Similar dictatorships arose in many Latin American republics.
This also probably explains why the United States has been so successful in spite of this apparent problem. Its strong culture of egalitarianism, and revulsion at the idea that one man should overstep his constitutional bounds, has kept its leaders from getting carried away with the pomp and circumstance of their office.
Besides this practical reason for separating the roles of heads of government and state, there are of course a few other pragmatic reasons commonly brought up for preserving monarchies. These are, for example, no need to have the head of government attend symbolic functions, a responsibility which the head of state (and/or his family, in the case of monarchies) can assume.
But still, the most powerful reason, I think, for the separation of real and symbolic power, is that it keeps power from going to one's head, so to speak. A Prime Minister cannot have delusions of grandeur (or at least has to try very hard to have such delusions) when on paper he serves a King or President.