Technically the Soviets did occupy certain small islands such as the Kurils, and the Sakhalin islands, as well as certain Japanese possessions on mainland Asia like North Korea, and Port Arthur; but I'm assuming you are meaning Japan proper, as in the home islands.
Well there is the obvious reason that the USSR simply didn't invade Japan, there are probably two reasons for this. One the USSR didn't have the ability to invade Japan, as the Soviet navy didn't really have the capacity to supply and invading army. Secondly, the USSR had suffered numerous casualties in their invasion of the island of Shumshu so its possible they were dissuaded from planning an invasion. So its different from Germany in that the Soviets couldn't physically invade Japan, so why would they get a piece? The Soviets had also contributed more to the defeat of Germany than Japan, so they "deserved" a piece, and its not like the allies could really stop them.
There was also another motivation from the Americans to rebuild Japan and shape Japan into a nation that would not only be a firm ally in their ideological struggle with Communism, but also make sure that their culture of militarism and expansionism that had led to the Pacific War would never be able to rise again. To this extent the USA didn't even give occupation zones to other western nations that were their allies. MacArthur was made "Supreme Commander" and was basically given near dictatorial powers to rebuild Japan. The international tribunal that prosecuted Japanese war criminals was made up of several judges from different nations, but besides that was primarily made up of Americans. So basically the Americans didn't want to split up Japan like Germany, because they wanted to be the ones to direct the rebuilding and reorienting of Japan.
For books, I'd recommend John Dower's book "Embracing Defeat."
It was.
I think /u/Toptomcat said it best, but I'll back him up with some references here. The Soviet Union did claim and keep territory belonging to Japan, specifically the southern half of Sakhalin Island and the Kuril Islands.
This division was first seen at Yalta, when the conference concluded that the Soviet Union would enter the war against Japan in exchange for a "sphere of influence in Manchuria following Japan's surrender. This included the southern portion of Sakhalin, a lease at Port Arthur (now Lüshunkou), a share in the operation of the Manchurian railroads, and the Kurile Islands."
The entry of the Soviet Union into the war was not fully determined until after the Potsdam Proclamation of July 1945, but Stalin had already begun moving soldiers and equipment eastward from Europe to be ready in any event. The Soviet declaration of war came less than two weeks after the Potsdam Declaration.
Now, the war ended in 1945, but the Treaty of San Francisco, which provided for postwar territorial claims in the Pacific, was not signed until 1951 and did not become effective until 1952.
The Soviet Union was not a signatory.
In a statement on the treaty, Soviet foreign minister Gromyko damned it as a separate peace, since it did not include Soviet or Chinese views:
"The Soviet delegation has already drawn the attention of the conference to the inadmissibility of a situation under which the draft peace treaty with Japan fails to state that Japan should recognize the sovereignty of the Soviet Union over the southern part of Sakhalin and the Kurile Islands. The draft is in flagrant contradiction with the obligations assumed by the United States and Great Britain with regard to these territories under the Yalta Agreement."
In 1956, the Soviet Union and Japan signed a joint declaration in 1956 that ended the official state of war between Japan and the Soviet Union, allowing diplomatic and consular ties to resume between the two countries. Despite this, Russia and Japan remain at an impasse over the issue of the disputed territories. The Japanese government has an excellent page devoted to the subject, but keep in mind that it is portraying only one half of a large argument.