From Discworld & Terry Pratchett Wiki
Wuffles was an extremely elderly wire-haired terrier, belonging to Lord Havelock Vetinari. Wuffles's fur was unkempt, and his teeth were broken. He had terrible halitosis, and spent much of his time sleeping deeply in a basket under Vetinari's desk, in the Oblong Office. Wuffles was a very old-fashioned dog; he thought of Lord Vetinari as his God. Wuffles was very loyal, and would try to bite anyone who's a threat to his God, even though his teeth hadn't been much use for years. In the tradition of the best mystery novels, Wuffles, a dog who cannot communicate with humans in an ordinary fashion, was a key witness in a high-profile crime, in The Truth.
Wuffles's first appearance was in Sourcery, where his loyalty to Vetinari even extended to the Patrician's temporary conversion to the form of a yellow-green lizard in a jar. Both dog and lizard were hidden for safekeeping by the Librarian. He also played something of a major role, as Second Canine Lead, in The Truth.
The sad news to report is that sometime between the events narrated in The Truth and the start of Making Money, Wuffles was escorted to the place where all good and faithful dogs inevitably go for eternal walkies. It had to happen: In The Truth Wuffles was 16 years old, which would make him over 100 years old in human years (according to the very suspect "1 year = 7 dog years" model). No doubt part of his conversation with Gaspode (which Gaspode has left uninterpreted) would have been a litany of complaints that puppies don't show you the respect they used to, these squeaky toys are not a patch on the squeaky toys we used to have in my day, call this a bone?, and these modern dogs who don't think of their God as being a God, show him the appropriate respect, why don't you!
Wuffles did make one more brief appearance, in the illustration of Lord Vetinari from Where's My Cow?. As this image is a product of Sam Vimes' imagination, it does not necessarily prove that Wuffles was still alive at the time Vimes concocted his urbanized revision of the story.
We are told in Making Money that Wuffles has been dead for over a year, and is buried in the Palace gardens where Vetinari (a man who normally shows no emotion) religiously visits the grave weekly to leave a favourite dog biscuit (one of Trucklement's Yummy Assortment. But never the yellow ones, as Wuffles hated those).
It is said that after the death of a favourite pet who is almost a family member, a decent length of time should be left before contemplating a replacement. After over a year without Wuffles, Vetinari is now at this point. Now get a copy of Making Money and read on...