Iraq didnt go from war to peace in May, 2003, it went from war to peacekeeping. The war had defeated Saddam Husseins government, and put it out of power. But the people who made Saddams dictatorship function were not gone, they were just out of work. They still had weapons, and they wanted their jobs back. For a few months, things were sort of quiet. And in that time, the coalition started work on repairing the damage done by several decades of mismanagement and grand theft by Saddam and his supporters.
What happened next is actually quite common in peacekeeping situations after a dictatorship is overthrown. Its happening right now in several parts of Africa, the Balkans, Latin America, Haiti and in Afghanistan. The losing factions decide that if they cant run the country, then no one else will be able to either. The gunmen and enforcers do what they were always good at, intimidating people and taking what they want. If they can intimidate enough people, they can take control of the entire country. But if there are some peacekeepers around, the bad guys just steal and terrorize. And wait for the peacekeepers to leave.
In Africa, the armed opposition is often tribe based. This is also the case in Afghanistan and Iraq. Ethnicity usually plays a major role, as does religion. In Africa, the tribes usually practice the same religion (usually Christian or Moslem), and this makes it easier for everyone to know whos on their side, and who to kill or pillage.
In Southeast Asia, militant Moslem groups see it as a religious obligation to kill and plunder Christians. In places like the Philippines, Indonesia and Thailand, armed Moslem gangs make raids on non-Moslem (usually Christian, but sometimes Buddhist as well) villages and kill and steal. In the Philippines, the Moslem gangs also kidnap for ransom. This technique has been very lucrative for some Moslem gangs.
In most cases, its all about money and power. Most people in the West dont realize that democratic government does not come easy. It requires the consent of the people, and a willingness to play by the rules. Those two conditions are very difficult to achieve in many parts of the world. Without a functioning democracy, you have a bloody game of king of the hill. While monarchies also work in several parts of the world (Nepal, Jordan, Saudi Arabia), they depend on brute force to back up the consent of the governed. Monarchs dont have to worry about elections, but they do have to worry about opinion polls. If they anger too many of their subjects, they can be removed. And usually means the death of the current monarch, as well many members of his family. This is what happened to the Iraqi monarchy in 1958. Its almost happened to the kings of Jordan several times, and the king of Nepal is fighting declining approval ratings with troops and riot police.
The cast of characters in Iraq includes small, but determined and heavily armed opposition groups representing the Sunni Moslems who long ran the country (under Saddam, several earlier dictators, the king, the British and the Turks before that), radical Shias who believe that a theocracy (let the clergy run the country) will solve all the problems, and criminal gangs. Dont underestimate the criminal gangs. They were always present, but they flourished under Saddam, who used them to keep the population terrorized, and to assist in some of his money making scams (especially during the UN embargo of the 1990s). Iraqis, in general, have never been enthusiastic about confronting groups of determined men with guns. Saddam took advantage of that to gain control of the entire country in the 1960s. His followers are trying to do it again. But theres the problem of those damn coalition soldiers, and the private security forces. There are also increasing problems with Iraqi police and security forces that are trained and organized to resist, and they are. But its a tough job. The Sunni and Shia gangs use threats against individuals, followed up with arson, beatings or murder as needed, to force people to support them, or not support the peacekeepers. As has been seen time and again recently, its up to the locals to decide if they will confront and defeat the thugs. If not, they are stuck with another dictatorship.
The situation in Iraq, and other parts of the world where there are Moslem populations involved, is complicated by the presence of Islamic radicals who are determined to destroy the non-Moslem world and bring Islam to the entire planet. The Islamic radicals complicate the matter by professing several positions that are illogical and untenable to Westerners (except for a few members of academia and the media.) The Islamic radicals justify their violence by claiming that the Christian West is making war on Islam. At the same time, the Islamic radicals insist that it is their religious duty to convert the non-Moslems in the West, and use any means necessary to accomplish this Holy Obligation duty. The Islamic radicals also insist that all the problems in the Moslem (especially the Arab) world (poverty, tyranny, lack of education and economic growth) are the fault of the West. Most people in the West disagree with this and point out that there is a distinct lack of personal responsibility in much of the Islamic world, and a willingness to just wait for good things to happen. Aside from the oil wells, not many good things are happening. Corrupt Moslem politicians steal much of the money, and use some of it to hire secret police and soldiers to keep themselves in power. Osama bin Laden began his career as a rebel by preaching against these corrupt Moslem rulers, but later decided that it was really the fault of the West that these gangsters were in power, so lets go after the West, destroy it, and everything will be better.
Sadly, the Iraqi situation is not unique in the world today. The factions still fighting for power are doing so at the expense of the Iraqi people. About a quarter of the billions being spent on Iraqi reconstruction goes to pay for security personnel. These mercenaries (as they are increasingly called by clueless journalists) have been very successful. Attacks on aid workers have not been very successful, and have declined. But attacks on Iraqis have increased. Coalition exhortations to Iraqis to step up and defend themselves is having some effect. Iraqi police and security troops have been increasingly effective (although their efforts usually only get reported when they screw up).
Peacekeeping is popular. It makes people feel good, both donors and recipients. But if often does not work, especially if the local population will not make a major effort in their own behalf. This has been seen in many countries in the last decade. Iraq will only get peace and democracy if enough Iraqis want it.