This is what we know about rat kings.
The term originated in continental Europe sometime before or during the 16th century. A mention of a kind of rat patriarch, fed and cared for by its nestmates, is recorded in Gesner’s Historia Animalium (1551-58), while the earliest report of the specific knotted tails phenomenon hails from 1564. A large number, sometimes up to several dozen, are bound together by their tails, which have become knotted and glued together with filth and calluses. If scientific analysis of preserved specimens is to be believed, the animals may live like this for quite a while.
Germany seems to be the epicenter of these phenomena and specimens continue to be reported, even into the modern era. The most famous specimen (held in the museum Mauritianum of Altenburg) dates from 1828. The last report came from an Estonian farmer in 2005. Like our little spooky film suggests, these creatures are often associated with bad luck and regarded as plague bearers. This may not be unfounded, as the high rat population density needed to form a rat king would also lend itself to the spread of rodential pestilences. The black rat seems to be the most common host, although brown rats, mice, and other rodents have also been reported.
The actual validity of their existence is questionable. Rats are, in fact, quite clean creatures and spent a lot of time grooming themselves. It is unlikely that their hygiene would be allowed to lax so far as to bind them together, even in cramped conditions. Furthermore, no living specimens have actually been delivered, only dead ones, raising the possibility that these are, in fact, man-made. The most likely theory is that these are hoaxes based upon skewed medieval reports. However, the idea is the perfect mix of sneakily believable, unsettling, and weird enough to pique our morbid curiosity, and has gained quite a place in pop culture and literature, featured in classic works such as The Nutcracker and in modern fantasy. China Miéville, Scott Westerfeld, and even Terry Pratchett have all touched upon it.
Sources: Neatorama.com, Wikipedia