Analysis: What's Up With the Title?
The title gets plucked from the end of Shakespeare's Hamlet, when the ambassador comes back and announces to Horatio and Fortinbras [standing amidst the dead bodies of Hamlet, Claudius, Laertes, and Gertrude (don't worry about the names, the point is there are a lot of bodies) that "Rosencrantz and Guildenstern are dead." Note that in Shakespeare's play Rosencrantz and Guildenstern don't even get the honor of being killed onstage. They are minor characters in a major sense. Audience members back around 1600 didn't shed too many tears over the two of them, but Stoppard makes these two the center of his play.
It also wouldn't hurt to note that the title is in the present tense – they "are dead." Does this mean they're dead at the beginning of the play, or at the end, or what? When did they die and how? Questions mount and we haven't even cracked the cover yet.