On my journey through the works of Shakespeare this week, as well as admiring his use of language, I'm learning to respect his knowledge of nature. His knowledge of birds is impressive and his references to plants read like a botanical encyclopedia. But I'm not convinced he was much of an entomologist. His knowledge of insects is pretty basic, even by modern standards, and he makes few attempts to distinguish individual species.
Still, he makes more than 100 references to insects and several more to spiders. But he divides them fairly baldly into goodies and baddies.
Let's start with the good guys. Bees are, of course, admired for their industry and organisation and increasingly valued for their pollinating services (take a look at the excellent Friends of the Earth Bee Cause " href="http://www.foe.co.uk/what_we_do/the_bee_cause_35033.html">Bee Cause campaign). There is a wonderful exchange in Henry V, where the Archbishop of Canterbury explains how honeybees provide an example of model government and social order, "Creatures that by a rule on nature teach the act of order to a peopled kingdom". Readers north of the border will be less impressed by references to the sneaky "weasel Scot" in the same scene, so I'll draw a veil over that. It's act 1, scene 2, if you're interested, just before the tennis balls arrive. Yes, really, tennis balls.
Bees are dangerous though, especially if their queen is threatened. When Duke Humphrey is murdered in Henry VI, part 2, Warwick declares that, "The commons, like an angry hive of bees that want their leader, scatter up and down, and care not who they sting in their revenge".
You'll struggle to find bumblebees in Shakespeare, as they are generally called humble-bees (a name that survived until comparatively recently - you'll find it in the works of Darwin too).  "Full merrily the humble-bee doth sing", says Pandarus in Troilous and Cressida. Perhaps Shakespearean bumblebees were just better at humming than their modern counterparts.
Ants are well-organised too, but he rarely mentions these. Apparently they only appear three times, and on one of these occasions, in the first part of Henry IV, the reference is to "pismires", an old word of Scandinavian origin. I won't go into too much detail here, but the name is evocative of the smell of the formic acid in an anthill, which was thought to resemble the smell of...well...work it out for yourselves. 
Wasps, of course, are characterised as angry things. Katharina in The Taming of the Shrew is a one-woman biodiversity action plan, as she is not only a shrew, but also a wasp. She warns Petruchio, "If I be waspish, best beware my sting". Good advice.
Butterflies, moths and their caterpillars occur frequently, but there is little attempt to distinguish one from the other, except that moths fly at night and eat one's clothes, caterpillars eat everything else, while butterflies are pretty and hard to catch. 
Richard II, the play that laments the state of England ("This royal throne of kings, this sceptred isle", etc), makes several references to caterpillars. A servant describes, "Our sea-walled garden, the whole land, is full of weeds, her fairest flowers chok'd up, her fruit trees all unprun'd, her hedges ruin'd, her knots disorder'd, and her wholesome herbs swarming with caterpillars". Saying that the kingdom is full of caterpillars is probably not a good thing, as the play in question was banned by Elizabeth I.
By far the best references to invertebrates appear in Romeo and Juliet, in Mercutio's description of the fairy Queen Mab: "Her wagon spokes made of long spinners' legs, the cover, of the wings of grasshoppers; her traces, of the smallest spider web; her collars, of the moonshine's wat'ry beams; her whip, of cricket's bone; the lash, of film; her wagoner, a small grey-coated gnat, not half so big as a round little worm pricked from the lazy finger of a maid;" This all formed part of Queen Mab's chariot, which was charmingly fashioned from "an empty hazelnut". With lines like these, is it really any wonder that Mercutio is apprently the Shakespearean character most loved by teenage girls?
But the real sign of the times is that the insects with which Shakespeare seems most intimately acquainted are flies (and maggots), fleas and lice. In Henry V, Falstaff is findly remembered for an apparently hilarious encounter with a flea, “Do you not remember a' saw a flea stick upon Bardolph's nose, and a' said it was a black soul burning in hell-fire?”
My, how we laughed...
And that (probably) completes our exploration of nature in Shakespeare's art.