Well, I think one of my favorite books at that age was probably something science fiction related, but these days theres a variety of things from which to pick, I think one of my favorites would be James Burke's "Connections" , another book is of course Sagan's "Cosmos" or these days I might even suggest something like Dawkins' "Climbing Mount Improbable".
I'm limiting my list to English books; I'm sure there are many non-English ones that are at least as worthy -- but that I'm wholly ignorant of:
Gray's Anatomy (ideally one would consult the 1858 and/or 1860 edition as well as a very recent one).
The King James Bible.
I don't know what to put as number three. A work that elucidates our technological progress seems called for, but I don't know if this is as good as the (first) series. A book that presents much insight into the human condition would make for a strong contender, so The Complete Works of William Shakespeare come to mind. OTOH, one of the books should really probe the depths of human depravity as well, so maybe Roots or Maus might be contenders as well. Just three books is a very small number to limit yourself to.