The types of natural beehives are really determined by the places bees decide to build their nests. Different locations require that the bees employ different techniques to make sure that their hive is safe and healthy.
Apis mellifera honeybees are very opportunistic. They basically look for a cavity in which to build a nest. In some cases, if they cannot find a cavity to build a nest in, they will build a nest under an overhang or some other protection.
A hollow tree trunk is probably the single most common nesting site for much of the natural history of the honeybee. Throughout the forests of Africa and Europe hollows in trees were the nesting sites of choice for bees.
Bees are fond of nesting in burrows of other animals. Creatures such as pigs, wild boars, aardvark, rabbits, and various others burrow underground. Bees can adopt these burrows and set up hives in them.