My apologies if you came here thinking this is an ad - but hang on, I may still be able to help you.
I think everyone who has ever been on the search for a purebred puppy has been told to find a "responsible breeder" - and that is excellent advice, since the other kind of breeder will just take your money, and either fail to provide you with a puppy at all, or provide one that is not healthy, not well socialized, and otherwise not well equipped to be a good pet. And when you try to ask questions or get help or *gasp* try to return your sickly puppy, you can't get any response from the breeder.
Responsible breeders put a great deal of thought, time, money, and effort into every litter, and they will provide support for the life of the dog. All this, for usually the same price that non-responsible breeders charge.
But how do you find a responsible breeder? They usually don't have puppies very often, and they usually have a waiting list before the breeding even happens. So they don't really advertise. So how the heck do you find them?
For all the bad things about the Internet and social media, the good thing is that it's a little easier to find responsible breeders. Of course, bad breeders have websites and Facebook pages too, but if you really pay attention you can tell the difference.
Things to look for:
1) What do they DO with their dogs? Besides breed them, that is? Look for breeders that show their dogs in some sort of event. It might be conformation shows which are the "beauty pageants" where an exceptional dog will attain a Championship or Grand Championship (abbreviated as CH or GCH before the dog's name). This competition proves that the dog meets the breed standard, and is reasonably physically and mentally sound. Or it might be some sort of performance event: obedience, agility, lure coursing, nosework etc. These titles come after the dog's name, and can sometimes look like a real alphabet soup! These events all demonstrate that the dog is trainable and physically sound, and usually speak to a good temperament. Sometimes, you find breeders who do actual work with their dogs (hunting, herding, search & rescue, detection etc) and that is probably the epitome of proving a dog's worthiness. Any breeder who does these things with their dogs will talk about it a LOT, will have photos and videos, and if you ask questions they will talk to you all day. Because this is their passion, their hobby, the thing that keeps them going. Non-reputable breeders will say things like "show quality puppies" but you will quickly find that they don't show their dogs at all. Which means they CAN'T know if their puppies are really show quality.
2) Membership in a national or regional breed club or kennel club. Again, if this is the case they will be very upfront about it. These kind of clubs are somewhat selective about who they allow to join - it's not elitism but rather they are looking for the same traits that make a responsible breeder: i.e. someone who truly cares about the dogs and the breed and is not motivated solely by profit.
3) Proof of health testing. Scam breeders have learned to say that their dogs are "health tested" but if you ask, you will often find that only means their vet did a normal exam. This is NOT breed-specific health testing!! Fortunately nowadays it is very easy to find out what testing has actually been done, and what tests are recommended for a particular breed. The Orthopedic Foundation for Animals started as a database for hip xrays to diagnose hip dysplasia. It has grown to a database for all testing for all breeds and the website is easily searchable. You can read what tests are recommended for a particular breed, and you can also see what tests have been done for a particular dog as well as for that dog's relatives.
Any responsible breeder will readily provide you with the link to their dog's OFA page. If you know the dog's registered name (like from an ad) you can search for it yourself. For example, our girl Ellie's page is here - if you look around you can see not only her test results, but the results for her parents, siblings and half siblings, and grandparents. If she ever has puppies their results will be available there too.
Over the years, irresponsible breeders have gotten smarter about using the "buzz words" that people are taught to look for when shopping for a puppy. They will put up fancy websites and sometimes steal pictures from the sites of responsible breeders. But if you ask about the 3 things above - and ask for proof which will be VERY easy for a reputable breeder to provide - that will go a long way toward saving you heartache and frustration.
In an effort to help people find responsible breeders of Great Danes, I have been updating the Breeder referral page on our website - you can find it here.
I hope this helps!