Elizabethan and Jacobean plays were often based on older ones, either classical or Italian, and were often collaborations between whatever playwrights could be enrolled to add a scene here or some dialogue there. Of course the greatest playwrights -- Shakespeare, Marlowe, Webster, Jonson -- could carry through entire plays on their own; but Beaumont and Fletcher, two of the greatest writers of the age, collaborated so closely that they are usually spoken of together. The plays of Beaumont and Fletcher rank higher than those of Beaumont, or of Fletcher, separately.

As with many writers of the period, we have only fragmentary survivals: some plays have been lost, others are of doubtful authorship, and first performance dates are known or guessed only imperfectly. The first Beaumont and Fletcher play was probably Philaster in 1609 or so. They produced some 12 or 15 joint plays over the next few years, their partnership being ended by Beaumont's retirement in about 1613.

Sir Francis Beaumont was a lawyer by profession and inheritance, born in Leicestershire in ?1584, studied at Oxford, and admitted to the Inner Temple in 1600. His most famous play, created in 1607, is the splendidly-titled The Knight of the Burning Pestle, which though traditionally regarded as the most famous Beaumont and Fletcher play, is now believed to be his work alone. After his retirement he lived in Kent until his death in 1616, a little before Shakespeare, and is now buried in Westminster Abbey.

John Fletcher was born in Rye in 1579, educated at Cambridge, and began to earn his living by playwriting in about 1605. He did write some plays on his own during his collaboration with Beaumont, and was successful on his own after Beaumont was gone. He also did a great deal of collaboration with many other dramatists; including with Shakespeare on The Two Noble Kinsmen, which certainly should have been included in Shakespeare folios since it was about half by him, and possibly to some degree in Henry VIII. Fletcher died of the plague in 1625 and is buried in Southwark, on the south bank of London.

Modern scholars being uncertain about so much about the pair, I've given up trying to create a full list of collaborative plays, but their works include, with approximate dates:

They are quoted in Webster 1913 as the source for numerous unusual words, including the famous unmorrised.

Sources included:
www.theatredatabase.com/17th_century/beaumont_and_fletcher_001.html
Some plays available on-line at:
www.theatrelinks.com/plays_playwrights/beaumont_fletcher.htm