English drama in the sixteenth century--usually under the title Elizabethan Drama because it roughly coincides with the reign of Queen Elizabeth I--is overshadowed by the plays of William Shakespeare, most of which were written in the last decade of the sixteenth century.
William Shakespeare (1564-1616), then, because of the stunning quality and quantity of his dramatic output, outshines other dramatists of the period who were often great dramatists. Shakespeare's plays encompassed comedy, tragedy, and history, and few dramatists of the even come close to such a broad range of drama. Of Shakespeare's plays, it's difficult to argue that one is the best, but among his best are Hamlet, King Lear, The Life of King Henry V, A Midsummer Night's Dream, and As You Like It.
Of Shakespeare's contemporary dramatists, perhaps the most important is Christopher Marlowe (1564-1593). Marlowe's most important plays include his first, Tamburlaine the Great, Parts I and II, and arguably his most popular play, The Jew of Malta. Both Shakespeare and Marlowe were actors and most likely knew each other quite well as fellow actors and rival dramatists.
Another of Shakespeare's contemporaries is Thomas Kyd (1558-1594 whose play The Spanish Tragedie became perhaps the best known of a genre of plays known as Revenge Tragedies (one of Shakespeare's revenge tragedies is The Tragedy of Titus Andronicus).
In the latter part of the sixteenth century, perhaps the most important of Shakespeare's rival playwrights is Ben Jonson (1572-1637), who wrote several comedies that are now known as Comedies of Humours, including Every Man in His Humour and Volpone, or the Fox, both of which are still routinely produced.
Other important sixteenth-century dramatists are Thomas Dekker, Thomas Heywood, George Chapman and John Marston, whose plays generally bridge the gap between late sixteenth and early seventeenth-century drama.