I see a small problem. Everyone here seems to assume that because clerics are the most powerful fighters and that they can heal people, they are the natural ones to take charge. This is emphatically not the case.
There can be a myriad reasons why clerics would not be running the show:
1. They are not the best leaders. Admittedly, they have above average Charisma and Diplomacy as a class skill. But aristocrats generally put their highest stat in Charisma and have an arsenal of social skills. Thus, the masses may be more inclined to follow the traditional aristocracy.
2. A good church would not abuse its power, or necessarily seek more. Someone cited the example that 'if your wife is pregnant and you don't want to risk her death in childbirth' then you would serve the clerics. Well, this seems strange. If the clerics are serving a good god, then surely they should help irrespective of the power that they garner (an evil church would be a different matter, but the original hypothesis is a good church). Granted, a good church has healing powers, but a good church would not abuse those to gain secular power.
3. Polytheism. The example of the Catholic Church's power of medieval Europe has been cited, but this is because it was monotheistic. In a (usual) DnD setting, there are multiple gods, and hence no single church would have nearly the same amount of influence. One could argue that as a result of living in an increasingly multicultural society, the power of the Christian Church over the West is in decline.
4. Neutral leaders. Following on from above, a single church would risk alienating other churches if it alone has significant secular power. In a polytheistic world, a neutral (say, aristocrat) leader may act as a unifying force: by not specifically adhering to any one religion, he allows all of them to live in harmony. (Of course, it is possible that have 'aligned' leaders *and* multiculturalism: e.g. the UK, which despite having an established Church of England still acts tolerantly to other religions.)
5. Traditional Reasons. People could follow their leaders out of tradition or a constitution. Just because clerics have power to heal and might on the field it does not mean that they would have overall control: they may play second flight to an ancient monarchy to whom the common folk have undying ancestral respect (for example).
6. Magic Saturation. In a high-magic world, it is possible that the novelty of the 'miracle' effect would wear off. If, tomorrow, the Pope (say) were to raise someone from the dead, then it would be a big bolster to Catholicism. Yet we live in a non-magical world ('fraid so, folks), so this would be 'out of the ordinary'. In a world where even the village cleric can heal mortal wounds, the mystery and marvelment at magic would soon fade.
Just six quick reasons why I feel not all countries would be theocratic. Feel free to demolish them!
Incidentally, medieval Europe was greatly influenced by the Catholic Church, but it was not a theocracy per se. The Church did not actually control the lands, but merely have a large amount of influence- and recalcitrant kings could always ignore that influence and advice.