EDIT: Here's the whole list, for completeness:
Clark, Civilisation
White, Medieval Technology and Social Change
McEvedy, Penguin Atlases of Ancient and Medieval History
Laslett, The World We Have Lost
Bernal, The Extension of Man
Franklin, Autobiography
Girouard, Life in the English Country House
Pirenne, Mohammed and Charlemagne
Runciman, The Fall of Constantinople
Cipolla, Guns, Sails and Empires
Hadas, A History of Rome
Oman, The Art of War in the Middle Ages
Vasari, Lives of the Artists
Bovill, The Golden Trade of the Moors
Caesar, Gallic Wars
Kuhn, The Copernican Revolution
mmorris answered this, but can I take this opportunity to add a couple of absolute gems, which I love, and which I have read and re-read so many times that I've gone through 3 copies each?
They are:
1. Dreadnought (by RKM)
2. Storm of Steel (by Earnst Junger)
3. (bonus) Josiah The Great: The True Story of The Man Who Would Be King
For my money, Dreadnought is the Best Overall History Book, and Storm of Steel is the best First-Person History Book.
They're topical, too -- SoS didn't have a quality English translation until 15 years ago, and Josiah The Great was based on the early-2000s discovery of a trove of documents that corroborated the amazing tales of the first American in Afghanistan, who became the inspiration for Kipling's short story (and John Houston's near-best-picture winner, and the movie Michael Caine says he wants to be remembered for), 'The Man Who Would Be King.'
