I've only read a fraction of the books written on the war/occupation of Iraq, and even those are a large pile. It's tough to choose the best one, but one of the most readable and informative has got to be "Red Zone: Five Bloody Years in Baghdad," by Oliver Poole. This is also perhaps the book most likely to engage war supporters and make them think without being didactic and without pulling any punches.
The title is accurate enough, but the book describes bloody and less bloody periods, and takes the reader all around Iraq, to neighboring countries, and to England. We see the war from the perspective of journalists, soldiers, and Iraqis from all sorts of backgrounds. We gain a better understanding of five years' worth of headlines as major events are incorporated in a tale of social changes and the experiences of individual characters.
Truly a brilliantly done book by a long-time reporter for the British newspaper, the Telegraph. Sadly, the Telegraph got a new editor and began insisting on pro-war propaganda. And sadly for us if not him, Poole settled down in England and started a family. So, the war goes on, short one reporter. And it didn't have many to spare.