I’d save the Shakespeare. While I don’t particularly care for Shakespeare, I know that millions do. People die every day, I think the odds are that the world would be better off with that body of inspiring work than the life of one anonymous person.
Definite vote for the Works, but I had to think about it.
My instinct is to save the person, but I can’t see any moral way to defend such a decision. Saving the person has a small probability of decreasing the net amount of suffering in the lifetime of the race (and a slightly smaller chance of increasing it).
Saving the contribution of an individual, (jokes about suffering of high school students aside) is far more important.
Given an opportunity to act rationally (not certain I would be rational) I would save the life works of a very very minor scientist rather than the scientist, unless there was clear reason to believe that their future works would be even greater.
I would save the person. The world, as a whole, wouldn’t be all that much worse off from the loss of Shakespeare’s works–there’s plenty of good literature out there. But a human life is inherently valuable (and no, I’m not religious, so that’s not part of my reasoning), and there’s no way I would be able to live with myself if I allowed someone to die to save an inanimate object.
So in a way I guess part of my answer is selfish–avoiding a lot of potential future suffering brought on by failing to save a living person.

I figure humanity has gotten this far without the complete, collected works of Sophocles, Aeschylus and Euripides; as well as countless other playwrights of whom we have precisely zero existing work. I’m sure we’ll get along just fine without yet another Bard.
This is … well … no hate to the OP, but it’s a ridiculous question.
Of course I’m gonna save the human being! There’s no debate, no issues, it’s a no-brainer.
I’m a pretty open-minded gal for the most part but I honestly can’t wrap my head around the answers of those who would save the books.
I love words, I love books, they make me happy. But we’re talking about a human life here, sheesh.
1970s saturday morning cartoons like Superfriends made me the kind of person who would save an anonymous human being. Shakespeare would have made me want to stand around and earnestly talk to myself about the tragic, unnecessary death of an anonymous everyman.
Even as someone who thinks Shakespeare is more overrated than The Beatles and Elvis x The Rolling Stones[SUP]2[/SUP], this is a no brainer. I’d save the thing of artistic merit that had already brought pleasure to millions. The anonymous human might turn out to be a right ungrateful git.
Sorry, but fuck Shakespeare. He’s dead and gone, his works pored over and analyzed to death.
The key here for me is anonymous person. You don’t know who that person is, what the world would be losing with him/her. Maybe it IS the next Hitler, or perhaps that person is going to cure cancer. I know the OP specified that this person is not going to do either of those things, that he/she is completely unremarkable, but you or I don’t know that. Maybe that person’s life will be unremarkable, but perhaps his/her children/grandchildren/great-grandchildren/etc. will be. My point is, Shakespeare is a known quantity. That anonymous person is not.
Wow, I’m surprised by the number of persons who would throw some other human under the train in exchange for some moldy writing/human product (sorry I know Shakespeare was great and all, but really, posterity would find some other hobby, I’m sure). Not to disparage anyone for their opinions, of course. First off, “Anonymous” people have helped me tremendously on many occasions. I can only return the favor. Secondly, if I was that “Anonymous” person, I would want to live and not die. This, in light of my respect for “the golden rule”, would give me another reason to not allow this anonymous person to die. Not to mention the fact that I do truly value the lives of others, even others who are more or less meaningless to me.
Follow-up questions:
Did you have to think at all about your answer? No.
Regardless of your own answer, how would you want another person in that situation to respond? I would hope that someone else would also save the anonymous person, but with the way society is going nowadays, I wouldn’t expect it.
If you answered “no”, is there any other concrete work of art or human thought (Beethoven’s symphonies; the periodic table; Euclid’s geometry; the Bible) that would make you answer “yes”, or at least give you pause? No. I love art and all, but how could it possibly be more valuable than one human life?
Shakespeare was unique and his works are hard to separate from his life; anonymous person A isn’t in any recognisable sense and has provided nothing of any worth, to our knowledge.
He may not have, but what of his children? Grandchildren? The son of someone his grandson saved?
I understand how some people enjoy Shakespeare’s work, but in the end, they’re just plays and sonnets. They aren’t important.
I would save the works of Shakespeare.
And then I would discover that I had been transported back to April 23, 1616 and that the anonymous person who I chose to let die was none other than Shakespeare himself.
And then, before I had the chance to read the works I’d saved, I dropped my glasses on the ground, breaking them. “Nooooo!” I would exclaim. “There was finally time!”
It was fortunate too, because As You Like It was really a cookbook!