Pretty much anyone who knows anything about Japan has heard of Yasukuni Jinja, the jinja in Tokyo enshrining Japan’s war dead, even if they know nothing about Shinto. The Gokoku Jinja, which also enshrine the war dead, are much less well known.
“Gokoku Jinja” means “Country Protecting Jinja”, and these jinja were set up by the government of Japan before the war. The idea of enshrining people who had died fighting for the Tennō first appeared among the people pushing to restore Imperial rule to Japan in the mid nineteenth century, and was put into effect by the government very soon after Meiji Tennō took authority in 1868: Yasukuni Jinja was founded (as Tokyo Shōkonsha — Tokyo Spirit Inviting Jinja) in 1869.
This seems to have inspired people around the country to create jinja to honour their local war dead, and quite a lot seem to have been created. The government was not happy with this, as they wanted to keep control of people’s memorialisation of war, and laws were passed forbidding the creation of Shōkonsha. (Religious freedom was guaranteed by the constitution, as long as it did not interfere with society, but Shinto was not a religion anyway, so laws could be made about it. There was a bit of casuistry going on here.) However, the government was keen to encourage people to honour the war dead, and generally be positive about being killed in war, so they kept, and supported, local jinja for this purpose: the Gokoku Jinja. It seems that they were not called that until 1939, with the name Shōkonsha being common earlier, and the final rationalisation may also have happened in 1939, because that is roughly the period when the Japanese government became really militaristic and authoritarian.
The basic rule seems to have been to have one Gokoku Jinja per prefecture, in the prefectural capital. So, for example, Niigataken Gokoku Jinja is in Niigata City, the capital of Niigata prefecture. (“Ken” is the Japanese for prefecture in most cases.) However, there are exceptions. For example, Hyōgo prefecture has two Gokoku Jinja, one in Kōbë (the prefectural capital) and one in Himeji, Hokkaidō has three (because it is enormous, I imagine), and neither Tokyo nor Kanagawa has one (probably because Yasukuni is so close). Perhaps there would have been one per prefecture if there had been more time for the system to be worked out. The Gokoku Jinja enshrined the war dead from their local area, typically one prefecture, while Yasukuni Jinja enshrined all the war dead. Thus, in theory, most of the war dead are enshrined in two places.
However, with Japan’s defeat in 1945, the Gokoku Jinja, like all jinja, were removed from state control, and there were real concerns that the occupiers would dissolve them. They were, after all, jinja dedicated to the war dead. That did not happen, and after the restoration of Japanese independence the Gokoku Jinja started working together. The Shinto establishment also seems to regard them as important, although not on the level of Yasukuni Jinja; there seems to be rather more attention paid to the Gokoku Jinja as a group than to other groups of similar jinja.
Today, there seems to be quite a lot of variation between them. Some, like Niigataken Gokoku Jinja, are large, and appear to be prospering. Others seem to be in trouble. They all have the problem that no members of the Japanese military or Self Defense Forces have died on active duty in almost 75 years, which means that the number of people with a personal connection to anyone enshrined there is small, and dropping. Obviously, I think the priests would all like this problem to continue, but it is one that they need to address. It appears that the more stable jinja are making an effort to strengthen their position now, by rebuilding their structures or publishing collections of memories of the war, while there are still people around who remember it. That is, of course, just a way of buying time. If you visit the homepages of the more active ones, they emphasise rites of passage, such as Shichigosan and weddings, and annual events such as Hatsumōdë, and do not emphasise the nature of the jinja very strongly at all. It will be interesting to see how these jinja evolve over the next couple of decades, as the last people who personally remember the war dead pass on.