Concerning the adaptation of one of Shakespeare's plays, it is legal to use his writing within a new play?

Question

In other words, a new play, new name, same story with modern additions, modern language, added new characters, but also with occassional lines from the original Shakespeare play?

Answer 1

Basically, yes, it's legally kosher.
Copyright law only applies to works for a certain number of years, though that number has been fiddled with a lot lately, largely to do with companies like Disney who have properties they still profit from but are getting up there in age. Otherwise those works no longer covered by copyright law are fair game to reproduce and distribute.
However, if you're going to literally reproduce another person's work, from a creative and professional standpoint, you should at least credit them for your new, semi-original work.

Answer 2

Yes, legally it's sound. Generally speaking, copyright laws protect an author's work until a hundred years after his death, but there are exceptions. Shakespeare, however, has been in the public domain for quite sometime. And if you had any doubts, just take a look at Tom Stoppard's acclaimed play, Rosencrantz and Guildenstern Are Dead. It's written about two minor characters of Hamlet and at times takes large chunks of that text verbatim to establish mood and scene.