The Rise of the West, by William McNeill, is a tour de force—the only true world history by a single author. Unlike Spengler and Toynbee, this is not one man's quirky vision, but an accurate summation of the human experience; it changed my understanding of history.
The Image, by Daniel Boorstin, explains the difference between reality and image in politics and daily life in a way that allows others not to be confused.
Exporting Democracy, by Joshua Muravchik, is a recent book that stands out. Muravchik turns what might appear to be a dry and self-evident topic into something fascinating and deep.
My own specialty, the Middle East, inspires more bad books than good ones (and they, of course, dominated the bestseller lists during the war with Iraq). Two classics are The Venture of Islam, by Marshall Hodgson, a three-volume survey of Muslim history that is original, quirky, and brilliant; and Islam in Modern History, by W. Cantwell Smith, who explains the profound trauma of Islam during the past two centuries and why it continues. I also recommend two recent studies: Culture and Conflict in Egyptian-Israeli Relations may not sound exciting, but this little-known study is Raymond Cohen's dazzling interpretation of political culture in diplomacy and the relations between states. The Closed Circle, by David Pryce-Jones, is a virtuoso indictment of what's wrong with politics in the Arabic-speaking countries.