That's a good question!
The title is inspired by two different sources: a mildly obscure piece of classical music and a science-fiction short story. The former is "The Unanswered Question" by Charles Ives; the latter is "The Last Question" by Isaac Asimov. While the story is a bit more literal (it's text, after all!), both have what might, at first, appear to be similar themes.
You can find a fun version of the Ives piece at the American Mavericks website, with a performance by the San Francisco Symphony and Michael Tilson Thomas. The Asimov story is available online at a site dedicated to the story, although I'm unsure of it's actual legal status.
You can read "The Last Question" for yourself. It's a bit more overtly religious than most fiction that I like, but it's a very satisfying short story. Indeed, it's reputed to be Asimov's personal favorite. The top level of the Multivax site is an amusing homage, but the question itself is a fundamentally meta-physical one. Physics has a clear answer: no. The details to explain that would take a while, so I'll let anyone interested ask, or Google for it.
The Ives piece is actually a bit more complex to explain. The piece itself is fairly simple, if unconventional. There's a soft continuum of strings that evokes a mildly exotic and spacious feeling. At intervals, a solo trumpet gives a simple set of notes that seems to be a question. A set of noisy and blaring flutes (yes, flutes!) answers the trumpet each time but the last. At the end, the trumpet's final question fades away, and the strings slowly fade to silence. Interpretations vary, but the general sense is remarkably similar to the Asimov story: a question is repeatedly asked, and never really answered in a way useful to the question's source.
There's a somewhat broader context here, too. At the time the music was written (1906), the debate between the two sides of classical music was ongoing. Should music be programmatic, as the Wagnerians thought, or entirely abstract, as espoused by the Brahmsian set? Ives, idiosyncratic as ever, seems to be saying "neither...and both" all in this one piece. To some extent, the entire piece is just an abstract work with no clear plot. On the other hand, it could be seen as literal. Indeed, the question in the title might be the larger question about the purpose of music, and the piece itself declines to answer.
None of this, of course, answers the question in the title of this blog entry. And, I'm not going to. You'll have to figure it out!