American post war planning was based on the assumption that many Iraqis would act in their own interest. The widespread looting and banditry, plus the collapse of the Iraqi civil service, left the US with a lot more work than they had planned on. This contradicts many pervious experiences (post World War II, post Cold War Europe), but was not totally unexpected. Iraq was known for its factionalism (religious, tribal, ethnic and political) and this, it turned out, resulted in a low (by Western standards) level of civic responsibility. A lot of Iraqis did come out to work for the common good, but many more did not, and these are the ones that make the headlines. Too many Iraqis were grabbing whatever they could, and too few were trying to protect public property. This was made worse by most Iraqis not even admitting this was a problem, and instead blamed the US for not promptly providing security (to protect Iraqis from themselves.)
There are still occasional attacks on coalition troops. Rifle shots and grenades for the most part, but very few casualties are caused. In some cases the culprits are caught and they usually turn out to be Baath party diehards or Islamic radicals from outside the country.
More deaths and injuries occur because of revenge killings among Iraqis. Many former Baath party and secret police officials still live where they always have, and their victims know that. Some of the Baath party members have formed militias for self defense and this has led to regular gun battles, particularly in northern cities, like Kirkuk, where exiled (or expelled by Saddam) Kurds have returned looking for revenge and their stolen property.