Meijin is a title in Japanese Go, written 名人. Its original meaning is "master" or "expert" or "virtuoso", and applies to any field, not just Go. Historically in Go, during the Edo period in Japan, there was only one Meijin, equivalent to a 9-dan rank.
The modern Meijin title came about in 1962, as a successor to the former title of Saikyo (1959-1961). The title is the now second most prestigious (at least in sense of prize money) in Japan (after the Kisei): the winner's purse is 36 million Yen.
The first-ever Meijin League was a 13 player all-play-all, completed in 1961/2. It has claims to be one of the outstanding tournaments of all time, involving as it did a high proportion of the world's leading players. It was won by Fujisawa Hideyuki, on an unlikely tiebreak. Results are here: http://gobase.org/games/jp/meijin-old/1/
The competition for the title is sponsored by Asahi Shinbun newspaper since 1976. Before that it was sponsored by Yomiuri Shinbun and was considered to be the most prestigious in Japan. The numbering of terms was started again with one when the Asahi took over sponsorship.
In Edo period Japan, there was an official government job for the Meijin Godokoro -- the famous expert Go tutor to the Shogun. (There was a similar job for the nation's best shogi player.) The godokoro post was supposed to be held by the undisputed strongest player in the country, who was appointed by the Commissioner of Temples and Shrines. In times when it was unclear who was the best player, the position was sometimes vacant. The Meijin title was a requirement to become godokoro, but didn't guarantee the appointment.
Strong and ambitious Go players sought the job, sometimes resorting to scandalous political maneuvers. The Meijin Godokoro had significant power, prestige, and perquisites, for he had a government stipend and some access to the Shogun. It was practically a lifetime appointment because the Godokoro was exempt from competing in the Castle Games, and indeed barred from serious contests (since he was theoretically supposed to devote his every effort to helping the Shogun be a better player). This made it hard for other players to demonstrate that they were stronger, and therefore the rightful Meijin.
Because of this and other governmental support for Go (i.e. the Four Houses), during the Tokugawa period, the quality of of play grew faster in Japan than elsewhere.
The last traditional Meijin was Shusai; though in fact the system had necessarily changed after the Meiji Restoration. After Shusai's retirement the title was vacant; the Honinbo title was contested. The rank of 9 dan was separated from the title, and promotion to 9 dan was awarded through the Oteai, the first being Fujisawa Kuranosuke.
John Fairbairn has written about this on the Mind Sports Olympiad site ( www.msoworld.com). Also, Ohira's Appreciating Famous Games provides some details, including a few games from the jubango that sometimes decided who would be Meijin Godokoro.
A list of modern Meijin title holders (to 2000) can be found at
http://www.msoworld.com/mindzine/news/orient/go/japan/_meijinsub.html .
The current holder is Cho U Meijin.
In 2003, Yoda Norimoto defended a challenge by Yamashita Keigo Kisei. A report of the action around the first game is on the homepage of Rafael Caetano.
In 2004, Yoda Norimoto Meijin was challenged by Cho U Honinbo. The games are both interesting and unusual - Yoda Meijin played an interesting move in game three and game four is even stranger - 29th Meijin - Game4.
Cho U won the title in six games.
There is a list of Edo period Historic Meijin.
Edited by Charles Matthews 2003-12-14, from contributions including those by moonprince, TakeNGive, and Tim Brent.