An entity created by taking a variably specified number of rats, for which the consensus number is taken to be 7a (the bad-luck number), and linking them together by tying their tails into a knot. This feat of applied and inventive cruelty to animals, if successfully completed, earns the perpetrator membership of the Inner Circle of the Ratcatchers' Guild where deep and secret lore is passed on.
In folklore, linking eight rats together by their tails is reputed to create a psychic link between the eight separate brains, which fall into synch and work together like a powerful organic computer, creating an entity greater than the sum of its parts.
This has been known to happen once on the Disc, when Ron Blunkett and Billy Spears, the rat-catchers of Bad Blintz, created their Rat King in an idle moment; only for the resultant entity to name itself Spider, and seek to take over all Ratkind, in a psychic explosion of fear and rage and dark violence.
Only Maurice and the Rat Clan saved the day, Maurice destroying the Rat King but losing a negotiable number of lives in the process.
There have been (scientifically unsubstantiated) examples of the cryptozoological phenomenon rat kings on Roundworld too.
Also, in the science-fiction serial The Ballad of Halo Jones (originally run in the comic 2000AD, and later released as a graphic novel), in a future interplanetary war, a Rat-King is used as the central processing unit in a supercomputer that works out and applies Planet Earth's military strategy. Halo and her buddies in the army are disgusted to discover their supreme commander really is a rat - or, in fact, five rats....