Well, for a variety of reasons. You have to remember the absolute devastation that occurred on the Japanese mainland. Even before the bombings of Hiroshima and Nagasaki, the Japanese suffered heavily from conventional bombing, fire bombing, and even famine. During the war, around 360,000 civilians died, which is fairly significant. Combine this with approximately 2,000,000 military deaths and you have a lot of dead people. The Japanese were willing to suffer a lot for what they believed and especially for the emperor, but the emperor had accepted defeat and surrendered.
Understanding all of this, the US decided to keep Hirohito on the throne and to punish the so called "war mongers", namely the Japanese high-command. This also worked due to the Kyujo incident, where members of the Japanese High Command and the Imperial Guard attempted to arrest the emperor and stop the surrender. This coup failed, yet it only angered the Japanese people and helped direct some of their anger at the Japanese military. So, in the end, the military hierarchy of Japan was crippled, yet the emperor was still in place. Although the Japanese were willing to fight and die ferociously and they put up a fight, they were tired of war, especially after suffering a series of defeats starting after Midway in late 1942.
So, in the end after the war there was no will to resist due to the emperor's acceptance of the unconditional surrender, the fact that the emperor was still on the throne, the long series of defeats they suffered at the hands of the allies, the significant casualties they took, the suffering of civilians, and finally the prosecution of the Japanese high command, which had been responsible for a failed coup against the emperor. Therefore, the Japanese people had no will to continue the fight after the occupation and there was no ensuing insurgency. Comparing Post-War Japan to Iraq is a bit wrong, as there are a variety of religious and ethnic groups in Iraq that have a history of conflict, whereas Japan does not.
I hope this helps. Also, this is my first time submitting a post here, so let me know if I need to fix anything/get better sources.
Sources:
http://www.historyplace.com/unitedstates/pacificwar/timeline.htm http://warchronicle.com/numbers/WWII/deaths.htm http://www.historylearningsite.co.uk/civilian_casualties_of_world_war.htm
The differences between Iraq in 2003 and Japan in 1941 are too numerous to count. The biggest difference, though, is that Japan is a nation-state whereas Iraq was created entirely out of imperialist ambition.
After WWI, the League of Nations divided the formerly Ottoman-ruled Arab areas of the Levant and Mesopotamia between the United Kingdom. France got Syria and Lebanon while the UK got Mesopotamia and the lands on either side of the Jordan River (Israel hadn't been created yet).
During the days of the Ottomans, what we know as Iraq was three vilayets (provinces): the Arab Shia in Basra, the Arab Sunnis centered on Baghdad, and the Kurds around Mosul. The Brits deciced to lump all three of these together into one country, called it Iraq, and then put a guy whose family was from Arabia on the throne of a country he'd never set foot in before (a common practice which was designed to leave the appointed ruler dependent on the imperialists). This king, Faisal, pursued a policy of pan-Arabism which left many ethnic minorities feeling excluded. As you could imagine, this left a very tenuous ethno-religious situation on the ground in Iraq.
Contrast this with Japan. Japan has been a unified country for hundreds of years, and went through a period of strong nationalism and modernization in the late 19th and early 20th centuries, almost at the exact same time as many western countries were experiencing similar movements. It's not a coincidence that the Meiji Restoration, the American Civil War, and the Franco-Prussian War all happened within the same decade. So, in a sense, Japan was already more like an industrialized western nation than any other country outside of Europe or North America.
The problem of insurgency never really took off in Japan because no one in Japan had a reason to buy into that idea. The people of Japan were still attached to their country, and to the idea of a maintaining a functioning society. They had seen the good that industry and modernity could do for their society, and believed that if they followed the law and went with the plan, so to speak, they could achieve peace and prosperity. It has since worked for them. Japan was (and still is) a highly-developed country with a government fully capable of financing itself, enforcing its laws, and maintaining sovereignty, by force if necessary.
You can't say the same for Iraq. Iraqi insurgents have no reason to support the system the US tried impose after 2003. They're actively trying to tear it down. Also, a lot of the people fighting in Iraq today aren't even Iraqi. Many of them are sponsored by private and governmental groups fighting for their own purposes.
That brings us to the next problem: the geo-strategic situation surrounding Japan vs. that of Iraq. Japan is an archipelago, and is only near to China, Korea, and Sakhalin, a disputed Japanese/Russian island thousands of miles away from Moscow. Iraq is right at the heart of the Middle East, surrounded by Saudi Arabia, Iran, and Turkey, who are all enemies of each other. The first two are actively waging a proxy war using Iraq as a battle ground, while the third shares a large population of Kurds who are more than willing to use the Kurdish areas of northern Iraq as a staging ground for their own struggle for independence.
So, in short, Japan didn't suffer from insurgency/terrorism in the wake the US's conquest because it was already a nation state capable of taking care of itself, whereas Iraq is a mess of a country stitched together by imperialist ambition that's being slowly pulled apart by stronger neighbors, each with their own host of issues.
edit: typos
The closest thing to an insurgency in postwar Japan was the activities of the Japanese Communist Party. Following surrender, MacArthur freed political prisoners, including the long-suppressed leaders of the nascent Japanese Communist Party. MacArthur had no intention of letting the Communists get a foothold, but the jailed leaders argued that they could form an alliance with the occupying Allies against Japanese fascist figures. MacArthur remained skeptical but he freed them anyway.
Once free, the Communists did try some low-level agitation. But MacArthur's media restrictions against Communist rhetoric pushed the effort deep underground. Meetings were held and regional candidates elected, and the Communists even won a few seats in the Dial with their "lovable Communism" approach.
But MacArthur was a tough nut. He stamped out communist media and writings and emboldened anti-communist political parties. He did everything he could to marginalize the communists. It worked.
Despite the revolutionary rhetoric and their overtures with Moscow, the Japanese communists never engaged in overt action against the Occupation. They knew that would lead nowhere. Instead, they went the democratic route and got trounced.
I'd argue two main reasons - that there remained a co-operative Japanese government after the surrender, and that there was no real desire to engage in insurgency.
The surrender of Japan did not involve the dissolution or collapse of the pre-surrender government. Rather, unlike Germany in 1945 (or Iraq in 2003 for that matter) where the existing government ceased to exist, the Japanese government remained intact and the Allied occupation authorities existed alongside it. In one sense, the Japanese 'collaborated' in their own occupation and were an important part of reforms undertaken and there was no need for violent resistance when there were other methods of making oneself heard.
There was also no real desire to engage in insurgency, as the military essentially had little or no sway after the surrender. Why listen to those who had lost the war and got you into the occupation situation in the first place? The armed forces were also rapidly demobilised and they co-operated fully in this - the 3.5 million troops in Japan on 15 August 1945 were all demobilised by the start of 1946.
John Dower, one of the most prominent historians of Postwar Japan and the Occupation actually weighed in on this issue in 2003 editorial. Although it verges on the polemical, Dower was prescient about the differences between Japan and Iraq. His main points are that Japan still possessed a state structure (mostly conservatives within the bureaucracy) in 1945 that collaborated with SCAP. This led to a rough synergy between SCAP and the conservative bureaucracy. Furthermore, SCAP itself had a New Deal philosophy that saw government as a solution (quite a contrast to Bremer) and thus had an incentive to create a strong national infrastructure. Finally, Dower notes that Japan benefited from an initial lack of outside economic interest, so the Postwar Japanese economy developed to suit the needs of domestic prosperity.
The Dower editorial has been archived by the Asia-Pacific Journal here: http://www.japanfocus.org/-John_W_-Dower/1624 and a more detailed paper here from History & Policy, http://www.historyandpolicy.org/policy-papers/papers/dont-expect-democracy-this-time-japan-and-iraq
In short, the extreme nationalists became outliers to the Japanese political system in a generation due to a government that saw it to be more advantageous to ally itself with the US and a larger population that saw the postwar economic prosperity far exceed anything achieved by the Imperial government.
What makes OP think that there maybe would be terrorists in Japan, since there are terrorist groups in Iraq? Why would that be the case? I miss the relation between the situations.