I think that purebred dogs are very important to our culture and society and responsible breeders definitely have their place. Here are some criteria that I think are important for responsible breeding and some caveats to that criteria.
1) As you mentioned, the breeder should breed to improve the breed. Anyone who breeds their dog should have a goal in mind, an "ultimate example" of the breed that they are striving towards. This example, however, should still fall within the breed's standards, so in my opinion some sort of competitive exhibition should be required. Conformation showing is a touchy subject and sometimes the extremes favored in the show ring do more harm than good (see American GSD's and Bulldogs for an example of this) but by and large conformation showing is one piece of the puzzle that is important for the maintenance of purebred dogs. Competitive sports like lure coursing, tracking, obedience, herding and agility are also essential to this. A purebred dog should be bred for function as much as form and I don't believe that any dog that hasn't proven that it can perform what its breed was meant to do should ever be bred.
2) Genetic and health testing is of utmost importance when you are evaluating a breeder. All dogs should be OFA and CERF cleared and tested for any disorders common to that breed such as von Willebrand's for Dobermans and such. The breeder should also know the health and genetic status of at least the sire and dam's parents, if not grandparents and farther back in their pedigree. It goes without saying that the dogs should appear healthy and clean and well-groomed and should be on heartworm and flea prevention and current on vaccinations, but this is not enough on its own.
3) The breeder should be open to questions and should also ask you a lot of questions. I'd be loathe to acquire a dog from someone who didn't basically put me through an interview to determine whether I am a responsible dog owner or not, and to make sure that I know what I am getting into with the breed of choice. This of course requires that the breeder knows the breed inside and out, the good points as well as the bad points, the kind of training to which they respond best, and any special requirements or added quirks of the breed in general. A person who will sell a dog to anyone with a checkbook and a leash and collar is not a responsible breeder. Likewise, the breeder should be open to fielding questions about their own breeding practices without getting snippy or defensive.
4) A good solid contract is often totally unenforceable in court, but I still think that it is important to set guidelines for a person purchasing a dog from you. A responsible breeder has a well laid out contract with a clause about neutering the animal unless it is specifically going to a home to be shown and possibly bred. They will only provide an AKC limited registration to help protect against unscrupulous breeding of their stock as they take pride in their kennel and their dogs. They will assist in rehoming a dog if the animal does not work out for any reason and they also be available for any questions or problems that you may have to try to ensure that they don't NEED to rehome the dog for a preventable reason in the first place.
I'm sure there are things I'm forgetting, but these are four major points that I feel are important in selecting a responsible, reputable breeder for your purebred dog of choice, and I do feel that these breeders play an important role in the world of dogs. Many of these responsible breeders are involved in breed clubs and rescues, so that's a good place to start to find one of them. They don't normally advertise in the newspaper or anywhere else for that matter, so you have to look more carefully for them, but they are there. Go to a dog show and meet one.
Backyard breeders and puppy mills can go right to hell though.