Wow, that's not an easy question to answer. Great breeders differ with the breeds that they're breeding.
And, if you're going with a breeder, go with a GREAT one, not just a "good enough" one. "Good enough" could cost you tons in vet bills.
Anyway, a great breeder will be honest with you. If you ask what types of health problems they can expect, they'll lay it all out and tell you what you can expect from THEIR lines.
Sometimes, even different lines of dogs have different health problems.
A great breeder will know everything about anything regarding their breed and will happily answer any question you ask. For example, if you were getting a golden retriever and asked how the breed came to be, a great breeder will tell you who bred to whom, what dogs were crossed and why, and how they started their kennel.
A great breeder will LOVE to talk to you all about your breed.
A great breeder will know what genetic problems to test for and will test for them in all of their breeding stock. In my breed, that means sub-luxation of the patellas, VWB (von willebrand's disease), PHPT (thyroid cancer), PRA (progressive retinal atrophy), alopecia X, and will have never bred a dog that has epilepsie.
A great breeder will title their dogs before breeding in some type of way. Either they will be performance tested, having sporting/herding/working/schutzhund titles or they will have conformation titles. Ideally, they'll have both.
A great breeder will make you sign a contract stating that you will spay/neuter the dog/bitch, that you will keep in contact with them, and that, if for any reason, you cannot keep the dog, that it will be transported back to them. Plus, they will guarentee the health of the dog for NO LESS THEN TWO YEARS.
I'm sorry, but a health contract for 72 hours is just stupid.
What all of this means for someone buying a pet is that their pet will be structurally sound and will live a long, active life and will LOOK like and ACT like the breed that it is supposed to be.
It will have tight feet and patellas so that it can romp and play and continue to be a sound animal until a ripe old age, etc. It will have a shorter back, so as to reduce and minimize back injuries. It's shoulders will have proper angulation to reduce wear and tear.
Its hips will not be disfigured with bad genetics, so that it will not be dysplastic as an adult.
It will have a solid temperment that is correct for whatever breed it is, so that you can trust the dog around strangers, other dogs, and children.
These are things that a normal puppy buyer won't know or even think about, but it makes all the difference in the life of your pet.
Not only that, but if you as a pet buyer have any questions about why your dog is doing this or that, or how to train them properly, or if you feel that something is not right with your dog, you will have a life time back up, friend, and resource.
THAT is a great breeder.