Greensleeves, is an Elizabethan period piece, that is sometimes attributed to King Henry VIII on his courtship of Anne Boleyn. You may often hear the piece sing a Christmas Carol under the hymn "What Child is This?". In 1934, Vaughan Williams arranged a Fantasia on Greensleeves that is often performed in orchestral manner. However you can find piano transcriptions of this fantasia and
here is Paul Barton, an Internet sensation himself performing the piece on youtube:
You can download the sheet music free of copyright (depending on your location) from the
Petrucci Internet Sheet Music Library Project.
For more information on the background and for more recordings read the Classic FM article.