In England, somewhere in the early 17th century, someone (we don't know who) wrote a ballad about Daphne and Apollo. The ballad tells the well-known tale from Ovid's Metamorphoses (book I, vss. 452-567): Apollo having spoken disparagingly to Amor, Amor takes revenge by shooting his golden arrow right into Apollo's heart. He's made Apollo fall in love with the river nymph Daphne, and he shoots at Daphne his arrow of lead: she won't love Apollo in return. Apollo chases Daphne while proclaiming his love and eminence and begging her to have pity on him. She hasn't. In her despair she asks her father, the river god Peneus, to take away her all too beautiful body. He does and turns her into a bay. Apollo embraces the tree, and her laurel leaves will henceforth be used to adorn the heads of the victorious. (The song has been recorded on the 'Van Eyck'-CD from Audivis). 
The Dutch poet Jan Janszoon Starter (ca. 1594-1626) was of English descent. He turned this song into Doen Daphne d'overschoone Maeght ('When Daphne, that most beautiful maiden'), and published it (1622) in the second edition of his Friesche Lust-hof, beplant met verscheyde stichtelyke minne-liedekens, gedichten, en boertige kluchten (Frisian garden of delights, sown with several edifying songs of love, poems, and jocular farces). 
Starter's version became a favourite with the Dutch public, and gave rise to a large number of contrafacts: songs with changed or completely new lyrics which used the melody of an older song. The song was immortalized by Jacob van Eyck (ca. 1590-1657), the recorder player, who published a number of variations in his Der fluyten lust-hof (The flute's garden of delights). The variations have been recorded by (among others) Marion Verbruggen. Finally, in the present century, Jetse Bremer arranged 'Doen Daphne d'overschoone Maeght' for a cappella choir (recorded on Komt Vrienden in het Ronden and present here as a midi file).
This process of contrafacture has been described by Louis Peter Grijp in his Het Nederlandse lied in de Gouden Eeuw. Het mechanisme van de contrafactuur (The Dutch Song of the Golden Age. The contrafacture mechanism). According to his book, a number of reasons account for the popularity of contrafacture in the Dutch 17th century. There was only a small number of able composers. Yet singing was a favourite pastime for the young and affluent youth of the Republic. A large number of songbooks was published in often expensive editions. This naturally led to reuse of existing melodies. Of course, for those without formal musical education, it's also a lot easier to sing to a tune which is already known. Finally, writers with religious intentions often wrote religious lyrics to existing songs, in order to replace the secular or worldly original texts. 

On these web pages, I have assembled some of the contrafacts written to the melody of 'Doen Daphne d'overschoone Maeght'. The preliminary work for this collection has been done by Ruth Van Baak Griffioen, who devoted her dissertation to an exhaustive investigation into Van Eyck's sources for Der fluyten lust-hof. She lists about 30 contrafacts to the tune, some of which themselves became sources for new contrafacts.
From those contrafacts which I have seen, I've tried to select those which have been recognizably influenced by Starter's lyrics. I have also tried to include a broad range of authors and subject matters. Of all contrafacts, I give both a literal transcription from the source and a modern Dutch version (in italics).
Included here are:

• Anonymous: A pleasant new Ballad of Daphne

This text is a version of the English song on which Starter was to base his adaptation. Ths version is from the Roxburghe Ballad Collection (I:388). I have copied it from Ms. Van Baak Griffioen's book. 
• Starter: Doen Daphne d'overschoone Maeght

Starters adaptation.
• Valerius: Men brand, men blaeckt, men schend, men moort

Adriaen Valerius (1575-1625) was a notary in Zeeland. Shortly after his death his Neder-landtsche gedenck-clanck (something like Dutch sounds of remembrance) was published. The book recounts the events of the Dutch revolt against Spain. The account is punctuated with songs, some of which were to become part of the Dutch national heritage. The song given here ('They burn, they schorch, they violate, they kill') tells of the reign of terror established by the duke of Alva in the 1668-1672 period, when the cause of the revolt seemed lost: 'Never so much rain was seen to drip from a roof, as one now sees people crying all day. Just Lord, look at us, and collect our tears in a vessel. Show us that you love the innocent soul which is ever kneeling before you'. The melody which Valerius used is slightly different from the one employed by Starter.
• Stalpart van der Wiele: Als Jola d'onberade Maegd

Johannes Stalpart van der Wiele (1579-1630) was a catholic priest in Delft - not an easy position to hold in the early Dutch Republic. He was a prolific writer of religious poetry and songs. He wrote at least two contrafacts to 'Doen Daphne d'overschoone Maeght'. The song which is given here ('When Jola, the unwise maiden', from the Extractum Katholicum) in its first two stanzas closely follows Starter's song, but Stalpart replaced Daphne with Jola (a silly girl), Apollo with Jesus, and Jola is fleeing 'into the world' while Jesus tries to save her. Like Apollo in the original song, Jesus tries to convince Jola by describing his nobility and magnificence. Unlike Daphne, Jola of course in the end succumbs to Jesus.
• Pers: David van Samuel gesalft

Dirck Pieterszoon Pers (1580-1662) was a printer, publisher and songwriter in Amsterdam. He was one of those who aimed to replace 'indecent' lyrics by more virtuous ones. To the tune of Daphne, he wrote a song 'David anointed by Samuel' (quoted here from the 1662 Vernieuwde (= 'renewed') Urania), based in part on the apocryphal Psalm 151. The song describes the early life of David in a pastoral setting, fighting with lions and worshipping God. God takes Samuel to David, and Samuel anoints David as the future king of Israel. 
• Krul: Iuffrou! waerom is't dat gy vlied

The only light-hearted contrafacts to 'Doen Daphne d'overschoone Maeght' which I have seen, were written by Jan Harmenszoon Krul (ca. 1601-1646). Krul was an Amsterdam playwright, songwriter and composer (one of the very few). He used the tune of 'Daphne' at least twice. In his play Alcip en Amarils (Alcip and Amarils), published in Minne-spiegel ter Deughden ('Virtuous mirror of love', 1639), the tune is used for a song which gives praise to an anonymous hero who has just beaten an infamous Spanish knight. Krul remained closer to Starter's text in 'Iuffrou! waerom is't dat gy vlied' ('Miss! Why is it that you're fleeing?', from Pampiere wereld, or Paper world, 1644). A lover is asking his (richer) beloved why she flees from him, but when she remains cool and aloft, he turns against her, and assures her he doesn't need her money. 'You were bred and raised in silliness. That is the title of which you are boasting'.
• Theodotus: Op de waerdigheydt vande aldersuyverste en alderheylichste Maghet Maria

Theodotus compiled Het paradys der gheestelijcke en kerckelijcke lof-sangen (The paradise of spiritual and ecclesiastical hymns, 1638). An appendix to the Paradys contains this song 'To the dignity of the most pure and most sacred virgin Mary'. The song itself is a compilation of many of Mary's traditional epithets.