To best understand bees, one needs to know exactly what a bee is. The answer is, at the outset, simple, but there are complications.
First off, bees are insects that belong to the order Hymenoptera, which includes ants, sawflies, and wasps. Studies of bee DNA have shown that they are in fact close cousins to modern-day wasps, with whom they share a common ancestor (i.e. a many-greats grandmother). In other words, bees are a kind of wasp. What distinguishes bees from wasps? Most of the time it is behavior: a bee collects pollen and nectar to feed to its young. Wasps capture insects for their young to devour. However, there are some wasps (Pseudomasaris) that have evolved to collect pollen for their offspring, and there is a group of bees (some Trigona species) that has evolved to collect rotting meat for their offspring. Behavior alone, then, doesn't separate all bees from all wasps.
Better put, then, bees are those wasps who share a common pollen-collecting ancestor. The descendants of this ancestor are said to all belong to the same 'clade*': Anthophila (which means flower-loving). Their pollen-collecting behavior has led bees down and evolutionary pathway that has resulted in furry bodies and pollen-collecting appendages, while the wasp's predatory lifestyle has led to long spiny legs and no need for extra hair.
A few groups of bees have given up collecting pollen and instead let other bees do the hard work for them. These 'cuckoo bees' lay eggs in the nest of another bee who does collect pollen. The cuckoo bee larvae destroy the 'host bee' larvae and then eat their pollen. Cuckoo bees tend to look more wasp-like as they have shed the hairy vestiture typical of pollen-collecting bees. Nonetheless, DNA analysis tell us that they share the same pollen-collecting wasp ancestor as other bees (they are in the same clade).
There are probably close to 30,000 species of bees around the world. 20,000 of them have been acknowledged by scientists, but many areas of the world have not been thoroughly sampled, and likely harbor species currently unknown to us. Contrary to popular belief, most bees don't live in hives. There is no queen. And they don't make honey. In fact, of those 20,000 known bees, only 7 are honey bee (Apis) species.
The majority of bee nests are in the ground, dug by bees who also collect pollen and nectar, and also lay eggs (functioning therefore as both queen and worker). The honey bee lifestyle we know so well is the exception rather than the rule for most bees.
* Think of a clade as an exclusive branch of a family tree. All descendants of Grandma and Grandpa Smith, for example; Grandma's sister's kids would not be part of the Smith Clade.