A triple ko is a game state where there are three kos on the board, all in play at the same time. They are typically part of the same configuration, as in this example.
Say you have the kos a, b and c. Black takes a, White takes b, Black takes c, White retakes a, Black retakes b and White retakes c, repeating the original position with the same player to play. Under the simple ko rule, Black could now retake a again, and the cycle would go on forever.
The postition where we started with reappears.
Under superko rules White is prohibited from playing , because that would repeat the original position. Instead, white can play a ko threat, and if black responds the cycle can start again (with at , and at being prohibited).
Of course, a process going on forever is undesirable. Traditionally, a triple ko meant no result, and was considered unlucky. Several modern rulesets handle it with a superko rule, under which it is similar to a regular ko.
An example of a triple ko that is not a single configuration is a simple ko with a double ko seki that each player can use for ko threats. Also see the O Rissei - Cho Chikun triple ko in the next diagram.
Here are the first three moves in that triple ko.
In December 2005, a triple ko occured in the semi-finals of the Samsung Cup in a game between Luo Xihe and Choi Cheolhan. The officials were already discussing the possibility of arranging an extra lightning game in case of a draw, when Luo Xihe elected to give up the large (23 stone) group involved in the triple ko in exchange for compensation elsewhere. It turned out that his counting was accurate, as he went on to win the game by 7.5 points.
Honinbo Sansa played a famous historical game involving a triple ko in 1582, against his rival Kashio Rigen. The game was played in the presence of Warlord Nobunaga at a monastery in Kyoto. Due to a triple ko, the game was suspended without result. The next day Nobunaga's ally Akechi Mitsuhide rebelled, surrounded the temple, and killed Nobunaga. After this, a triple ko was considered bad luck.
On June 28th 2007, during the 14th Agon Cup in Japan, a game between Kono Rin 9p and Akiyama Jiro 8p ended in a no result due to the emergence of a quadruple ko. From the inception of the Nihon Kiin on 24th July 1924 till 30th June 2007, there have only been 19 instances of no result recorded. Of the 168 813 games played by Nihon Kiin professionals in this period, only 19 have yielded no result, averaging about 1 no result game every 9000 played. (Translated from an article in Weiqi Tiandi 2007.15). Hence if you cannot find too many triple ko games, do not get too disheartened, they are rather rare. For a list of 15 triple kos, see Triple Ko.
- 1724-04-27, Inoue Shunseki - Nagano Kaizan? 
- 1970-09-16, Fukui Masaaki - Cho Chikun
- 1975-07-10, Cho Chikun - Kato Masao
- 1980-05-25, Matsuoka Akira - Yanagawa Hiromasa?
- 1984-05-24, Qjan Yuping? - Katoka Satoshi?
- 1985-05-28, Liu Xiaoguang - Awaji Shuzo
- 1989-01-28, Kono Mitsuki - Kurotaki Masanori
- 1993-09-02, Komatsu Hideki - Rin Kaiho
- 1998-10-14, O Rissei - Cho Chikun
- 2002-03-15, Qiu Jun - Yu Bin
John F. Re "the" historical game - what are you referring to? The linked site clearly says 1724 then the lunar date.
Harleqin: Sorry, I made the footnote clearer now.
John F. I'm still none the wiser - the players are the same.
Harleqin: Um. No, they are not. One says "Sansa - Rigen", the other "Inoue Shunseki - Nagano Kaizan".
Bill: The link is to the 1724 game, despite the URL.
You obviously have the GoGoD version since you use our dating, but the year's the same either way.
Harleqin: I think I have most of these games from Jan van Rongen's "Friday Night Files" site and from gobase. I use the dating I like, in order to sort my records chronologically.
I say "the" because it's not the only historical game - there is also Sekiyama-Ito. We can't claim to be complete, but as a benchmark you may wish to note that GoGoD has 12 triple ko games, 10 quad ko and 2 chosei (not quite all on the CD yet). We have a note of a quintuple ko in an amateur game in Japan, but haven't seen it yet. Can anyone construct such a monstrosity?
Harleqin: Is that a rhetoric question? It seems rather trivial. Forcing one in a real game is, of course, another thing ;).
Chris Hayashida: I don't know about the quintuple ko, but when I hear of a historical game with a triple ko, I think of the one played by Sansa and Riken the day before Nobunaga was betrayed. It was also referenced in the Hikaru no Go manga. I suspect this is the "historical game" that he is referring to. I don't know what the date is of that game, nor do I know if the web site is correct.
 RobertJasiek: Such a configuration is not consistently called "triple ko". It can also be called "position with both a basic ko and a double ko seki". Regardless of what the ko shapes are called as shapes, their behaviour might be similar to that of a triple ko shape. So one might speak of a "triple ko behaviour" although one does not need to call a "triple ko shape" where there is none.
This is from the match Gu Li vs Li Zhe 2011.09.04 during the 13th Chinese City League