Any folk songs from his plays? How about "Under The Greenwood Tree". Pete Seeger did a setting of "Full Fathom Five".

And as for a bawdy line, how about this exchange between the Nurse and Mercutio in Romeo and Juliet:

Nurse God ye good morrow, gentlemen.

MERCUTIO God ye good den, fair gentlewoman.

Nurse Is it good den?

MERCUTIO 'Tis no less, I tell you, for the bawdy hand of the dial is now upon the prick of noon.