Druids can shape into swarms, but only a couple
The wild shape ability states, in part:
At 4th level, a druid gains the ability to turn herself into any small or Medium animal and back again once per day. Her options for new forms include all creatures with the animal type. This ability functions like the beast shape I spell, except as noted here. The effect lasts for 1 hour per druid level, or until she changes back. Changing form (to animal or back) is a standard action and doesn’t provoke an attack of opportunity. The form chosen must be that of an animal the druid is familiar with.
Swarm is a subtype, not a type, and there are a number of animal-type creatures with the swarm subtype, such as the rat swarm and bat swarm. Since an [animal] swarm is a creature with the animal type, a druid familiar with a given [animal] swarm can wild shape into one starting at 4th level assuming they meet the rest of the requirements. In actuality, however, they will not be able to shape into any swarms until they can shape into tiny animals (6th level), since no published animal swarms are bigger than tiny.
Remember, also, that the ability functions like the beast shape line when an animal is chosen, and that beast shape I states:
When you cast this spell, you can assume the form of any Small or Medium creature of the animal type.
and beast shape II increases this to:
This spell functions as beast shape I, except that it also allows you to assume the form of a Tiny or Large creature of the animal type.
Which includes swarms. However, turning into a swarm, much like turning into anything in pathfinder (short of PaO) doesn't actually grant you the important parts of what you are turning into, most of the time. Remember that when you wild shape, most things stay the same.
"But aren't swarms lots of creatures, rather than one?"
Each creature has one type, which broadly defines its abilities. Some creatures also have one or more subtypes.
Which makes it clear that creatures are what have types. Furthermore, from the Swarm subtype:
creatures with the swarm subtype don’t make standard melee attacks.
which makes it clear that creatures with the swarm subtype are, in fact, creatures in their own right (in addition to being a collection of creatures).
If you do houserule that a swarm is not a creature, be aware that the consequences will be far-reaching and strange. Since everything permanent in the rules is either a creature or an object, many rules won't apply to swarms. For example, the swarm subtype provides rules that protect swarms against creature-targeting spells, which is made irrelevant if swarms are not creatures. For example, a non-creature swarm with a hive mind is immune to creature-targeting mind-affecting abilities because it is not a creature. And, while 'A swarm can occupy the same space as a creature of any size, since it crawls all over its prey' a swarm can't necessarily occupy the same space as another swarm, since they are not creatures. This means, for example, that a cat swarm may be unable to attack a rat swarm because it must enter its opponent's space to attack and is unable to do so. Also, this means that swarms count as unarmed opponents, since they are not a creature with an innate attack form. And furthermore, while "If your target is two size categories larger than the friendly characters it is engaged with, [the shooting into melee] penalty is reduced to –2", "There is no penalty for firing at a creature that is three size categories larger than the friendly characters it is engaged with". And so on.
Basically, everything physical in Pathfinder is either a creature or an object, and while there are edge cases swarms are not one of them. Swarms are creatures by the RAW and changing that will break huge portions of system. It makes far more sense to just houserule wild shape and beast shape if that's what you don't like.
"Oh, but swarms are creatures (or, rather, groups of creatures), they just aren't a creature"
This doesn't actually fix anything. A collection is not its parts, and so swarms being a 'group' doesn't actually fix any of the problems caused by them not being creatures. A group of creatures still doesn't count as a creature for the purpose of targeting rules, combat rules, templating rules, etc. If this seems confusing to you, I recommend you read up on intensive v.s. extensive object properties.