For me, the best description of an often overlooked aspect of Shakespeare's art, the songs, is found in the 1974 Norton Anthology of English Literature (M. H. Abrams, general editor):

"The plays contain some of the finest songs ever written. They are of various types: the aubade, or morning song, the gay pastoral invitation, love songs of various kinds, the ballad sung by wandering minstrels, and the funeral dirge. They illustrate many sides of Shakespeare's genius - his incomparable lyric gift, his ready humor, and his marvelous sensitivity to the sights and sounds of English life, especially the life of the country."

I would add that another aspect of Shakespeare's genius that the songs exemplify is the way that they foster creativity in others. The primary reason for this is that no musical notation survives for them, only the words, and so for each production they must be set to music before they can be sung. Therefore, like every other aspect of Shakespeare, they lead to work, learning, creativity, fun. Here is a setting for one of the songs from the Stratford Festival's 2005 production of As You Like It, wonderfully scored by ex-Barenaked Lady Steven Page: http://www.youtube.com/watch?v=BAqCw1jD1vU, and here are the words:

SONG

Blow, blow, thou winter wind,

Thou art not so unkind

As man's ingratitude;

Thy tooth is not so keen,

Because thou art not seen,

Although thy breath be rude.

Heigh-ho! sing heigh-ho! unto the green holly.

Most friendship is feigning, most loving mere folly.

Then, heigh-ho, the holly!

This life is most jolly.

Freeze, freeze, thou bitter sky,

That dost not bite so nigh

As benefits forgot;

Though thou the waters warp,

Thy sting is not so sharp

As friend rememb'red not.

Heigh-ho! sing, &c.