What dog breeds are the healthiest?
Depends on how you count it.
Longevity in dogs is tied very closely to size. If you’re looking at longevity only, then you’re going to be left with all small and toy breeds (at least looking at the averages).
The Life Expectancy of 165 Breeds of Dogs
You could also control for size and look for the outliers on longevity.
(note that the source matters for this data, and there are many studies that have found different numbers: Lifespan)
But, is living longer the best measure of health?
We could also look at the rates of diagnosis of certain diseases or disorders, but I don’t know of great data for that. Perhaps a better method would be to look at what kills dogs in the end - that is, do dogs of that breed tend to die from more generic “old age” complaints or from disorders likely to be breed-specific and cause problems long before death? Some data sets exist for that (Methods and mortality results of a health survey of purebred dogs in the UK - PubMed) but I don’t know of any studies that drew conclusions across many breeds from it.
One huge thing to note is that a lot of dog deaths aren’t due to health problems, but due to behavioral ones (Bad dogs die young, many from euthanasia, British study says). These behavioral problems are largely a result not of the breed but of poor breeding practices that don’t consider temperament, and of breeders who place dogs into homes where the owners are not suitable or prepared for that particular dog’s temperament and needs.
When looking for a dog, you should look first for fit - can you properly care for a dog with these traits? Will the dog and you both be happy together? And, if you are getting a dog from a breeder instead of a rescue/shelter, then make sure that the breeder is a good one doing the recommended health testing and proving temperament in suitable ways regardless of the breed that they are producing.