Maybe it's just because Fifi and Rex are always close to hand for ad hoc analysis, or maybe it's because cats have so obviously already hit the pinnacle of development and ceased to need any changes, but dogs have always been an example pointed to by both sides of the evolution debate. Evolution advocates point to them as an example of selective forces (with dog breeding, man-made selective forces) changing population characteristics. Evolution opponents have come from both sides: Some arguing that the fact dogs haven't split into separate species shows that speciation via selection is impossible, others arguing that the level of genetic diversity in dogs is too great to be the result of random mutations, and thus points to some other force at play. The poor dogs, meanwhile, are too stupid to pick up on any of this but happily offer their loyalty and frisbee fetching skills to all comers.
However, some recent genetic research sheds a bit of interesting light on the evolutionary history of dogs. Researches sequenced the mitochondrial DNA of several breeds of dog, plus modern grey wolves, to which dogs are believed to be closely related. Their results suggest that modern dogs were domesticated and removed from the wolf gene pool about 15,000 years ago, very recently by an evolutionary timescale. However, during that time dogs have built up and retained far more minor genetic defects than the wolf population -- and also much more genetic diversity (thus allowing all the different breeds of dog).
The researches believe the cause of this is that with human care, genetic changes which might have reduced a wolf's chances of survival are allowed to flourish among the dog population because they receive human care, and are thus under less pressure from natural selection. Thus, the modern genetic diversity among dogs is primarily the result of human care. I hardly think this is what the Discovery Institute had in mind, but we now seem to have found a population whose current genetic makeup is the result (in part) of intelligent design -- or at least of pampering.
UPDATE: Razib has some additional thoughts on dogs and human influenced evolution over at Gene Expression.