Indeed, greensleeves is a very beautiful song. It uses a rather common melodic structure; this can be found in many other pieces from the Renaissance. The melody also follows has an iambic pentameter, which is why many other lyrics seem to fit into the tune so well.

This is one of my favourite songs on the guitar as well... it can be played in many different manners, from tremolo to fingerstyle to harmonics. IIRC, has a channel just for Greensleeves renditions and nothing else.