As a scholar who has done a lot of research on the history of film censorship in Japan, I like to remind people that censorship takes many forms and need not all be state centered.
The Asahi reports this morning that one of the theaters scheduled to show the Oscar-winning documentary The Cove has broken under pressure from right-wing organizations and decided not to show the film. The right-wingers, who had threatened to begin protests on the 4th in front of the theater, had already performed loud protests in front of the distributor in April, charging those associated with the film with being "anti-Japanese" and "terrorists destroying the Japanese spirit." Theater N in Shibuya, which is owned by the publishing distributor Nippan, decided after consulting with the police not to show the film for fear something might happen to one of the customers or someone in the building. Cinemart Roppongi, the other theater scheduled to show the film, is considering whether to go on with the screening.
There is also a short article in Japan Today.
While it is hard to ask businesses to stick to their guns when right-wingers come out with their huge sound trucks blaring threats at rock-concert levels, but giving in to their pressure only encourages them. The theaters who stuck it out when the right wing threatened to stop the release of Yasukuni ended up getting very good business.
I might add that we should also remember that accepted consensus opinion can also be a form of censorship. It is interesting coming to Japan from America and seeing how dolphin and whale hunting, which are "obviously" wrong to most Americans and their media, are now seen as "obviously" right to most Japanese and their media. Some might say that is because the Japanese media is censoring other opinions, but Japanese would say the same thing of Americans. One of the important experiences in living multi-culturally is seeing how what is considered "natural" and "obvious" in one country is not considered that in another. It makes you realize how much the "obvious" is a cultural construction and is only possible by censoring the other as "obviously" wrong. I as a whole object to whale and dolphin hunting, but I don't think it is obvious. Those who think their side is obviously right are more often than not engaging in a kind of self-censorship that, while not involving obnoxious sound trucks, can sometimes be as odious. I think The Cove should be shown in Japan not because it will show the Japanese what the "truth" is, but because it will introduce the other into a situation where only the self reigns and start undermining the "obvious." Occasionally that needs to be done in America as well. Only then can real debate begin.