The Academic Ranking of World Universities (ARWU), out of Shanghai, China, has its merits: it comes out in August, and when differences across universities are not statistically significant, it places them in a tie rather than letting the chips arbitrarily fall where they may.
This year's list is somewhat kinder to Japanese universities, which clearly still dominate their designated region, the Asia-Pacific.
Full information is at the links below. The quoted material after the links highlights how Japanese institutions did in the top 200. Nine make the list. To summarize, Todai/U. of Tokyo is number 20 worldwide and top in Japan and Asia. Japan's number 2, Kyodai/Kyoto U., is still in the top 30 at a respectable 24.
Despite all the government money now going to Waseda and Keio, no private university is in the top 200 (the main weakness: science and technology). This is really a list of elite national universities (now 'national university corporations' or 'NUCs') in Japan. However, it is important to note that most NUCs are not elite, and it's interesting that the top universities in Taiwan and S. Korea were also national universities (of Japan--national imperial universities!).
in top 100
20 The University of Tokyo Asia/Pacific 1
24 Kyoto University Asia/Pacific 2
75 Osaka University Asia/Pacific 6
79 Nagoya University Asia/Pacific 7
84 Tohoku University Asia/Pacific 8
in top 200
101-150 Tokyo Institute of Technology Asia/Pacific 10-18
151-200 Hokkaido University Asia/Pacific 19-26
151-200 Kyushu University Asia/Pacific 19-26
151-200 University of Tsukuba Asia/Pacific 19-26