Photo: Naturkundliches Museum Mauritianum Altenburg [wikipedia]
Rat King doesn't mean the King of Rats, rather it is a medieval legend of what happened when a lot of rats get entangled at their tails, became stuck together and thus had to live as a giant rat ball entity. The cryptozoological curiosity became famous in Germany, with sightings as early as the 1500s. Not surprisingly, a large ball of gnawing rats was interpreted as a bad omen.
The Mauritianum museum in Altenburg, German, even has the mummified specimen of 32 rats shown above. Though scientists are skeptical of the authenticity of the specimens (rats don't normally become entangled, even when living in cramped quarters and no living rat kings have ever been sighted), the phenomenon lives on in pop culture, and after seeing this image, in my nightmares.
Link [wikipedia] - Thanks elzo!
If that's not gross enough for you, check out this video clip previously posted on Neatorama: World's Worst Mouse Plague: Millions of Mice Attack Australia
And btw, old mr. Pratchett does his homework before writing, so it's not "just like" in there. :)