What is the biological family that includes all bears?

The biological family that includes all bears is Ursidae.

Ursidae is the scientific family of living bears, whose members are commonly called ursids. Modern classification recognizes eight living bear species, including the brown bear, polar bear, American black bear, sun bear, sloth bear, spectacled bear, giant panda and Asiatic black bear.

Bears are part of the mammalian order Carnivora, but that does not mean every bear eats mostly meat. The polar bear is highly carnivorous, the giant panda specializes in bamboo, and most other species are flexible omnivores. Their shared family traits include broad bodies, plantigrade feet, five non-retractile claws and an exceptionally strong sense of smell.

Ursidae belongs to the dog-like carnivoran branch, Caniformia. Bears are therefore more closely associated evolutionarily with dogs, seals and weasels than with cats. Red pandas and raccoons may be called bear-like in casual language, but they are not members of Ursidae.