In point of fact, rat kings may have been a rare phenomenon in which rats forced to live in extremely overcrowded conditions became entangled at the tail and scrabbled out dim and desperate lives as a group. Verified, modern evidence of such a phenomenon does not exist, but we know they were widely exhibited historically in Europe and have reportedly been found in recent times (per the Wiki: "the most recent find dating from April 10, 1986, coming from a French discovery in the Vendée, and from January 16, 2005, coming from an Estonian discovery in Võrumaa").
Of course natural rat kings may be just one more confabulated lusus naturae, crafted for the sake of exhibition coin. Only 30-50 gained repute for supposed authenticity back in "the day." Per the Wiki, the "earliest report of rat kings comes from 1564."
The Wiki (linked above) makes these interesting points about the rat king's historical reception:
"Historically, rat kings were seen as an extremely bad omen, particularly associated with plagues. This is a reasonable conclusion if they are formed naturally, since large populations of rats housed in insufficient space generally bring with them disease and pestilence. With an increase in the size of the rat population comes an increase of the chance of outbreak of disease — for example, the Black Death, which is spread by the rats’ fleas.
The term rat king has often led to the misconception of a king of rats. This idea has been particularly appealing to the literary and artistic mind set: The Nutcracker, by Pyotr Ilyich Tchaikovsky, is set to a tale by E. T. A. Hoffmann, which features a mouse king as the villain. Another example is the fairy tale Rattenkönig Birlibi, by Ernst Moritz Arndt."
The following example of a mummified, naturalized rat king, housed in a scientific museum (The Mauritianum) in Altenburg, Germany, is not for the weak of stomach.
The Museum of Natural History in Nantes, France also houses a rat king, which was featured in its Naturalist Illustrations exhibit. The online catalogue includes an x-ray of the grouping:
A similar find, in Rucphen, Netherlands, occuring in the 1960s is also available x-rayed on the web, and includes a detailed close-up of the tail knot:
The Lewis Room, a small online, popular wunderkammer by Steve Lewis (1997), offers a brief account of the rat king, with an interesting citation from More Cunning than Man: A Social History of Rats and Men by Robert Hendrickson (New York: Dorset Press, pp. 92 - 93), which spaken so:
The name rat king may come from the old superstition that an aged wise rat sat on the entangled tails of rats and was treated as royalty by the pack. But it could just as well derive from an early belief that the animals entangled were one organism, a supreme rat with many bodies. Rat kings range in composition from 3 - 32 rats, with most consisting of 5 - 10 animals, and are apparently found only among the long and less pliable tailed black rat species, although a few verified rodent kings of squirrels and several unverified mice kings have been reported. Brown rat kings have been induced in the laboratory. Rat kings fabricated by tying the tails of live rats together look nothing like real kings, but rat kings have been created in the laboratory by gluing the tails of rats together; this causes the rats to become so entangled while trying to extricate themselves that a true knot is formed. Yet no zoologist has been able to prove exactly how rat kings are formed in nature. It is possible that the tails become entangled when the rats huddle together facing outward for warmth and security, urine and feces from those in the upper circle falling onto the entwined mass of tails. Other possibilities are that the tails might become entangled while the males are wildly fighting for females, or during mass grooming, or in the nest shortly after birth, or after the tails of a number of rats come into contact with some sticky substance. It may even be that the "verminous vermicelli" are formed in several ways. The rat king remains as much a mystery to nuclear-age scientists as it was to medieval peasants."