One of my first Golden Retriever males that I had years ago was a very athletic dog. He loved to run, play, and hunt. But there was one problem I kept running into with him: when we would go out in the field to play, his dewclaws were constantly getting caught and ripped. I had to repeatedly bandage his legs to keep infection and inflammation away. After that, I decided I would cut off the dewclaws on my future puppy litters. Leaving them just wasn't worth risking future damage to their legs.
In case you are wondering what a Dewclaw is, it is a claw that most dogs are born with. It's kind of like a thumb on their ankle (letter D in the picture). For most dogs, it will never be a problem, especially if it is a toy breed of dog. But if it is an active dog, a dog that might be used for outdoor sports, it can be a problem, as I testified earlier.
Removing dewclaws is usually done 3 days after the puppies are born. They are easily snipped off, there is little blood, and the puppies heal with no scar.
For confirmation show dogs, removing their dewclaws is generally not encouraged, and honestly, it is not needed. They are show dogs! What high energy athletic activities are they going to be doing?
For family pets, it also is not really necessary but one never knows if the family will like taking their dog out on nature walks where his dewclaw could get caught on something as simple as a fallen tree branch and rip it. So that must be kept in mind.
For working dogs though, especially those that are hunters, I see it as necessary to remove their dewclaws to avoid ripping them and suffering damage later on, ending in a veterinary bill to repair or remove them, leaving scars.
So, I remove the dewclaws on all of my puppies, except for small runts in the litter, to avoid this possible risk. I see it as a necessary health consideration for my Golden Retriever puppies.
Now, if I ever start raising some little dog breed, like Pomeranian, I really won't worry about removing their Dewclaws... I'll be more worried about keeping the little barkers quiet!