Many of us have a pet rabbit. Are there domesticated hares?

No, this rabbit is the closest thing to a domestic hare: Belgian Hare - Wikipedia. read more

I imagine there could be, though I have not heard of it. Wild rabbits and probably hares too, don’t do well in captivity. read more

No. Rabbits and hares are genetically incompatible. There is domestic breed of rabbit called a Belgian Hare, but this is a misnomer — it is a rabbit, not a hare. Fun fact: domestic rabbits and wild American rabbits (cottontails) are also genetically incompatible. read more

The Belgian Hare is not a true hare but rather a "fancy" (i.e., non-utilitarian) breed of domestic rabbit that has been selectively bred to resemble the wild hare. Averaging 6–9 pounds (2.7–4.1 kg), the Belgian Hare is known for its slender and wiry frame and its long and powerful legs. read more