Wuffles' entry in the Discworld Companion is as follows:Lord Vetinari's pet dog. A small, toothless and exceedingly elderly wire-haired terrier with a bristly stub of a tail, who smells bad and wheezes at people. He also has halitosis.Wuffles has stirred quite a bit of discussion in his time. He first appeared at the same time as Lord Vetinari, in Sourcery. During the course of that book, it was noted that he had no teeth, and posessed a growl that could raise the hair on the back of your neck and set off the "run for the trees!" instinct in the primate part of the brain. For several books, he was nowhere to be found, and there was some worry that perhaps he had gone to the great doggie kennel in the sky.
However, he reappeared and saved the day in The Truth, where we learned a little about how he views the world (he's an old-fashioned dog, and refers to Lord Vetinari as "God") and discovered that he does have teeth. Since, as Mr. Pratchett has said, there are no inconsistencies in the Discworld, only alternate pasts, one may safely conclude that Wuffles does have teeth, and that Sourcery merely took place in an alternate past.
This has not stopped a number of other theories from making themselves heard. These theories have ranged from "Wuffles is a vampire" to "it's actually Wuffles II." I think both of these in particular may be safely discounted - the first is rather absurd, and the second is nonsensical. Wuffles is 16 in The Truth, and there hasn't been enough time for Wuffles II to age that much since Sourcery, let alone since the last time he was mentioned.
Regardless of the Wuffles'-teeth controversy, the little dog does serve an important purpose: besides being a faithful companion for Lord Vetinari, in a literary sense he represents his Lordship's ability to care for creatures other than the city. Wuffles represents Lord Vetinari's humanity.