The Fools often sang witty little tunes to entice laughs and smiles from their benefactors. Indeed Feste and Lear's Fool both sing the same tune in their respective plays:
When that I was and a little tiny boy
With hey ho the wind and the rain
A foolish thing was but a toy
For the rain, it raineth every day.
Perhaps the best known song from the Shakespearean cannon comes from As You Like It.
It was a lover and his lass
With a hay, with a ho, with a hay-nonie-no
With a hay, nonie-nonie-no.
And this play have many other tunes laces through out frolicking in the forest.
Twelfth Night is the other play with prominent music with the tunes "O, Mistress Mine," "Come Away Death," and the whole theme of Orsino's melancholy being accompanied by music.
And there is also the melancholy - Desdemona sings "Willow" when she anticipates her husband coming in to kill her.
While often over looked, the music in Shakespeare's plays adds a delightful note to the lyrical poetry and human interaction.