Short answer for the overwhelmed readers with little time on their hands: Yes, some do.
The process of stinging and dying is called autotomizing and only various honey bees are susceptible, not honey wasps or yellowjackets or the Honey Nut Cheerios bee. Here’s how it works: When the bee stings you, its stinging apparatus screws into your skin like a corkscrew. The bee is too weak to pull it out without tearing its abdomen apart. Interestingly, when the bee stings an animal or insect with skin much thinner than human skin, it can easily pull out and fly off without dying. This does not apply to queen honey bees, which have no barbs in their stinging apparatus and therefore do not autotomize. Male honey bees, called drones, also kill themselves during copulation with a queen bee as their genitalia are ripped from their bodies mid-air during intercourse. (Rough!) Life isn't so good for the drones that don't mate with the queen either. Worker bees feed the young drones until they are ready to mate. Those that don't mate with the queen get kicked out of the hive and starve to death. Good times.