Mr Fusspot
Quite possibly the most important, and certainly the richest, dog in Ankh-Morpork. His mother was a pedigreed spoon hound. His father was, due to the nature of Discworld genetics, all of the dogs that his mother met after getting out one night. This dog is of such importance that there are quite a lot of people who want to see him dead, and the sooner the better. He was formerly owned by Topsy Lavish who, in the will dictated from her deathbed to Mr. Slant, in the presence of a legally binding number of witnesses, bequeathed him into the care of the Master of the Royal Mint.
The double whammy, for the Master, is that the dog is personally worth $AM20,000 (to be paid in arrears) for every full year he remains alive. The dog is also worth $AM100,000 to the Assassins' Guild, who are under orders to inhume the Master, should any unfortunate accident befall the dog. Fortunately the Assassins have a code of conduct, or the general Ankh-Morpork ethos might suggest, to an Assassin of a certain turn of mind, that to kill the dog himself and thus activate the deferred contract would be worth a cool hundred grand. Indeed, as Vetinari points out, somewhat acidly, Moist has been done a great favour here, as the Guild of Assassins will not accept a second contract on his life.
Mr Fusspot is notable for being the only small lapdog to ever tree Angua von Überwald in her werewolf form. The strange and unique circumstances in which he manages this are related in Making Money.
At the conclusion of the book, Mr Fusspot leaves his temporary abode with the Master of the Mint, and finds another home with a kind and appreciative new Master.
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Bizarrely, on Roundworld, New York hotelier and real estate billionaire Leona Helmsley left $12m (£5.97m) to her pet dog, Trouble. Good name. The pampered pooch received the largest bequest from Mrs Helmsley's will. Mrs Helmsley, who died in August 2007, was dubbed the "Queen of Mean" by the US media, and was known for her tough approach to business. She and her late husband, Harry, built a company which managed some of New York's most prestigious addresses, including the Empire State Building, as well as hotels across the country. The money for Trouble's upkeep was left in the hands of her brother, Alvin Rosenthal, who himself inherited $10m. See more here: [1].
There is also a German movie with Heinz Rühmann from 1953, where Rühmann as Briefträger Müller (Postman, sic Miller) inherits a small dog owning a fortune, bequeathed by a rich lady. See more here: [2]