It actually comes as "another" method of pest regulation: Ratcatchers.
During the Victorian era (1837-1901), in England, ratcatchers had a LOT of work thanks to the topic mentioned at this post (yes, hundreds of years later, the overpopulation of rats and lack of cats could still be felt).
There was a particular breed of rats in the Island: The brown rat. This "little" (it actually was quite large) fella could have 15000 descendants in a year if not controlled! Ratcatchers found out that they could make their work worth double benefits, not by simply catching rats, but also selling them as "participants" in a rather cruel entertainment: Rat-Baiting (just like a cock fight, but with no feathers... And an eager dog in the middle, anxious for some rodent blood).
Following the line of "make your work worth more", they also started selling them as pets (they were large!)
Jack Black was the "official" queen's ratcatcher, he had a thing for "specially attractive" rats and bred them to become gifts for pretty women.
There were high class "clubs" of people that had rats as pets, and also some museums!
Some people still do like them as pets. Derived all from that story I just wrote that could've made an article by itself :p... they even have websites.
http://www.nfrs.org/