I rescue dogs from the humane society as a hobby and have done this for a dozen years or so. Over the years we have fostered many cross-breeds that we tried to give a designer dog type name because it helps to market them. I'm sure that is how they originally came into being....someone wanted to sell dogs and they did not even have a male and a female of the same breed, much less take the time and care that should go into producing a pedigreed show quality litter (if you are thinking of breeding dogs responsibly).
I would not want to give money to people who mix breeds on purpose this way as I also work for a veterinarian and have seen puppy mills who sell designer dogs and would never want to pump money into that industry. The whole point of pedigreed show dogs is that you can predict the size, coat, temperament and other characteristics of a dog that you choose at birth. Designer dogs will have characteristics from differing parents so they will not be predictable!
Those comments aside, dogs of cross breed heritage, meaning the cross of two purebreds, can often be a great dog. I'm not fond of labradoodles myself because of the ear problems we see in a vet clinic, but mixes that I've found dogs of these mixes to be awesome: Labrador-chessie, rottie/aussie, pit/boxer, labrador/basset, shepherd/rottie, and we also had a pugle, which is pug/beagle, and he was a nice dog.
My husband disagrees with me and likes labradoodles, but he did not like the puggle. We placed a ridgeback/labrador with a family that could not decide if they wanted a ridgeback or a labrador, so she was a great compromise. We own a ridgeback/pit ourselves and a karelian bear dog/heeler whom we of course highly prize as much as our purebred rhodesian ridgeback and purebred golden retriever, who have had many health issues. My bear dog mix actually survived lymphoma. My favorite dog is a mix that we will never know WHAT she is....we call her a wonder dog....we will always wonder what she is.
Finding and choosing a dog should be about making a good match for your family. At the same time you want to make sure that the wrong people do not profit. If you are patient, good dogs of unusual mixes can be found. The rottie/aussie we placed was with a family that had been searching for that specific mix. The labrador/chessie was not a foster dog, but rather a personal dog we got from the humane society. He was one of the best dogs I have known and would have paid good money for him had I known, but got him for something like 50 dollars. We also adopted a purebred rhodesian ridgeback from a ridgeback rescue because we could not afford a purebred puppy and she ended up being the most expensive dog we have ever owned due to medical issues . But in the end, we loved her so much we would have paid it twice over. But with both we felt good when all was said and done, they would not have had their lives without us and they made our lives richer being in it. But they were the right fit for our family so they were priceless.