There are too many dishes to be listed, but here are those who spring to mind : tantanmen, miso ramen, jajamen, tofu gratin, katsudon, soborodon, kaisendon, hijiki, sushi, negitoro maki, subuta...
I guess most people don't know half of them, as they are either home-cooking (hijiki, soborodon...) and thus difficult to find in restaurants, or not so common for foreigners (tantanmen, jajamen, which are kinds of "ramen", the first is in red hor soup, the second without soup, but to dip in a thick meat-ginger-bambu sauce).