One "easy" way to kill a bear is to go hunting with at least two dogs and unleash them, when the bear charges you. The dogs will fight the bear allowing you to strike him without getting hurt.
Alternatively, bears can be killed or incapacitated using a spiked pit trap. These work best when placed on the bears regular paths, indicated by their large, distinct paw-prints, and baited with food bears usually seek out, such as raw fish, meat or berries (during summer).
Their skins can be made into fur, and bear fur has the highest overall defense values out of all furs, making it the best material for clothing you expect to get into a fight in. Bears give around 300 (As of v3.16, a small bear gave 104 cuts of meat and a normal sized bear gave 164 cuts) cuts of meat. Their meat is also as nutritious as Salmon, where 1 cut of bear meat is roughly equal to 1/3 of a Salmon, making bears the overall most rewarding animal to hunt. Their meat is also incredibly filling, and if prepared by smoking, can go bad before the entire stock is finished.
As of v315p1: bears remain one dangerous group. Even trapped in a pit, they still can fight back if you stand in their reach, and take 10 arrows from northern bow to die.
As of v3.19 - 3.20 when you fight the bear directly and have wounded him badly there is a chance he will flee from combat thus giving you a chance to finish him with your bow or run away to safety.
As of 3.50 beta bears, along with some other animals, can sometimes be found with their young. The saying "like an angry, mother bear" should not be taken lightly.