Updated 2010
Rankings are given from several sources, the first follows on below from 4ICU which differs from the traditional Kawaijuku rankings:
1. Keio University
2. The University of Tokyo
3. Waseda University
4. Osaka University
5. Hokkaido University
6. Tokyo Institute of Technology
7. Hiroshima University
8. Kobe University
9. Kyoto University
10. Nihon University
11. Meiji University
12. University of Tsukuba
13. Doshisha University
14. Hosei University
15. Tohoku University
16. Kyushu University
17. Japan Advanced Institute of Science and Technology
18. Nagoya University
19. Tokai University
20. Chuo University

Source: 4 International Careers and Jobs website 741 local universities are ranked at this website.

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Kawaijuku’s Rankings:

In 2001 the Ministry of Education sought to strengthen the “Top 30″ universities by changing the funding model. Various “Top 30″ lists that were floated at the time, but Kawaijuku prep school’s is probably by the most well known one in terms of the overall general public standing and reputation of universities.

2006 Ranking of National Universities by Subject and Average Admissions Score on National University Examinations (based on four factors: research funding (Kaken only), citations of research publications, entrance exam difficulty, and a reputation survey).
1 Tokyo
2 Kyoto
3  Osaka
4  Tokyo Institute of Technology
5  Tohoku
6  Keio
7  Kyushu
8  Nagoya
9 Hokkaido
10  Tsukuba
11 Kobe
12  Chiba
13 Waseda
14  Hiroshima
15 Kanazawa
16  Okayama
17 Tokyo University of Science
18  Tokyo Metropolitan University
19 Tokyo Medical and Dental University
20  Osaka City University
21 Niigata
22 Kumamoto
23 Tokushima
24 Osaka Prefecture University
25 Gifu
26 Tokyo University of Agriculture and Technology
27 Yokohama National University
28 Yamaguchi
29 Nagoya City University
30 Kagoshima

Yoyogi University Prep School rankings:

Yoyogi college preparation (or cram) school — possibly the nation’s most famous and relied upon by academics — produces a series of annual rankings of public and private university departments based on the average score that students must earn on the national university admissions examination for entry.

Law & Economics: Tokyo 1/93% Kyoto 2/91% Osaka 3/90% Nagoya 4/89% Hitotsubashi 4/89%  Kobe 5/87% Kyushu 8/86%  Tohoku 8/86 Yokohama National 11/84% Hokkaido 13/83% Nagoya City Osaka City 13/83% 15/80% Kanazawa 15/80%

Art & Literature: Tokyo 1/91-93% Kyoto 1 91-93% Ochanomizu 2/89% Osaka 4/88% Hitotsubashi 5/88% Kanazawa & Nagoya & Kobe 10/86% Osaka City Yokohama National 14 / 85%
Science & Engineering Tokyo 1/92-94% Kyoto 3/91% Osaka 5/89% Kyushu 6/88% Ochanomizu 6/88% Nagoya & Osaka City & Nagoya City 9/86% Tohoku & Kobe & Hokkaido 11/85% Yokohama National & Kanazawa 14/84% Medicine Tokyo 1/95% Nagoya 2/94%  Hokkaido & Kyushu 3/94% Kyoto & Osaka 3/93% Kobe & Osaka City & Nagoya City 8/92%

(Schools are ranked and beside the ranking is the average of each university’s department rank. Only the top 16 universities for each departmental league table were considered.)

Ranking 2006 for private universities:

Schools are ranked by department in the Yoyogi ranking. The ranking above is an average of each university’s department rank (in three departments).
Law & Economics: Keio & Waseda & 1/69 Jochi (Sophia) 3/65 Doshisha & Chuo 4/64% Ritsumeikan & Rikkyo 7/63% Tsudajuku 9/62% Meiji & Aoyamagakuin 10/61% 12 Gakushuin 12/59%
Art & Literature: Waseda 1/69% Keio 2/69% Int Christian U & Jochi (Sophia) 3/63% Tsudajuku 6/62% Rikkyo 7/61% Doshisha & Chuo & Nanzan 8/60% Meiji & Kansai Gakuin & Aoyamgakuin & Gakushuin 11/59% Science & Engineering Keio 1/64% Waseda 2/63% Doshisha & & Tokyo U of Science ICU 3/60%  Jochi & Meiji 6/59% Ritsumeikan 8/58% Rikkyo & Kansai Gakuin  9/57% Tsudajuku 11/56% Aoyamagakuin & Nanzan 15/55%

Medical, dental, pharmacy, agriculture: Keio 70 – Jikei University 67 – Osaka Medical College  67 – Nippon Medical School  66  – Juntendo 65 – Kansai Medical University 65 – Kurume 65 – Iwate Medical University 64 – Jichi Medical University 64 – Kyorin 64 – Showa 64 – Tokyo Medical University 64 – Tokyo University of Science 64 – Aichi Medical University 64 – Kinki 64

Other rankings maintained by Asahi Shimbun and Recruit Ltd that indicate the quality of institutions are not displayed here. There are also other lists of top Japanese Universities, some broken down by field of study, and which are provided by World Education Services on their Japan page.

Regional and international standing of Japanese universities (these differ considerably):

Webometrics Top Asia Universities are ranked as follows:
1 University of Tokyo 54;  2 National Taiwan University  70; 3 Kyoto University 89; 4 National University of Singapore  111; 5 Beijing University  112
6 Chinese University of Hong Kong  123; 7 University of Hong Kong  148; 8 Hebrew University of Jerusalem  153; 9 Keio University 165; 10 Tel Aviv University  202
11 Weizmann Institute of Science  225; 12 University of Tsukuba 234; 13 Technion Israel Institute of Technology  236;    14 Tsinghua University China  238; 15 National Chiao Tung University  239; 16 National Sun Yat-Sen University  242; 17 Nagoya University  256; 18 Osaka University  266; 19 Tohoku University 284; 20 Shanghai Jiao Tong University

but according to 4ICU’s rankings …

Keio University ranks 6th on the Asian universities ranking page after 5 Chinese universities, while University of Tokyo only comes in 18th followed by Waseda University in 28th place. (this page refers)

The following rankings compare regional and world rankings of Japanese universities to those around the world:


Shanghai Jiao Tong University’s list of the Top 100 Asia Pacific Universitiesgives the rankings as follows:

Regional Rank Institution* Country World Rank (On the left:regional ranking, Right: world ranking)
1 Tokyo Univ Japan 14
2 Kyoto Univ Japan 21

3 Australian Natl Univ Australia 53
4 Osaka Univ Japan 54
5 Tohoku Univ Japan 69
6 Univ Melbourne Australia 82
7 Hebrew Univ Jerusalem Israel 90
8 Nagoya Univ Japan 97
9-17 Hokkaido Univ Japan 101-152

9-17 Kyushu Univ Japan 101-152
9-17 Natl Univ Singapore Singapore 101-152
9-17 Tel Aviv Univ Israel 101-152
9-17 Tokyo Inst Tech Japan 101-152
9-17 Tsukuba Univ Japan 101-152

9-17 Univ Queensland Australia 101-152
9-17 Univ Sydney Australia 101-152
9-17 Weizmann Inst Sci Israel 101-152
18-21 Natl Taiwan Univ China-tw 153-201
18-21 Seoul Natl Univ South Korea 153-201
18-21 Univ New South Wales Australia 153-201
18-21 Univ Western Australia Australia 153-201
22-37 Chinese Univ Hong Kong China-hk 202-301
22-37 Hiroshima Univ Japan 202-301
22-37 Hong Kong Univ Sci & Tech China-hk 202-301
22-37 Indian Inst Sci India 202-301
22-37 Keio Univ Japan 202-301
22-37 Kobe Univ Japan

Sources:
Your best reference online on selectivity rankings might be those maintained by WENR World Education News & Reviews but they go only up to 2006.
Shanghai Jiao Tong University’s list of the Top 100 Asia Pacific Universities
Webometrics Top Asia Universities
For a source of rankings for universities in various countries is the University of Illinois’ College and University Rankings Page

Source: 4 International Careers and Jobs website see ranking of 741 local universities at this website.

Other references:

Ichiryu daigaku: top ranking universities in Japan explains the importance of ranking universities in Japanese society.