Baghdad Sketches by Freya Stark — Stark traveled Iraq in the 1920s and 1930s when it was a newly created British mandate territory. Her account of Baghdad, the rivers, and the people is warm, precise, and still vivid. A good companion for anyone visiting the country.
The Demonic Comedy: Some Detours in the Baghdad of Saddam Hussein by Paul Roberts — A Canadian journalist's dispatches from Saddam's Iraq. Dark, clear-eyed, and often grimly funny about a country in the grip of a peculiar kind of totalitarianism. Useful context for understanding what preceded the 2003 invasion.
Guests of the Sheik by Elizabeth Warnock Fernea — An American anthropologist's account of living in a traditional Iraqi village in the 1950s, following her husband's fieldwork. A rare close-up portrait of rural Iraqi life from an outsider perspective, still widely read and respected.
Drinking the Sea at Gaza — For broader regional context, several books cover the Mesopotamian legacy.
The Great War for Civilisation by Robert Fisk — A long, angry, essential account of the modern Middle East by a veteran correspondent who covered Iraq across decades. Not an Iraq book specifically, but the chapters on Iraq are among the best journalism written about the country.
The Bookseller of Kabul and similar works capture the feel of a society under pressure; for Iraq specifically, Night Draws Near by Anthony Shadid is the finest piece of reporting from the early years of the 2003 occupation — a Pulitzer Prize-winning account told through the lives of ordinary Iraqis.
Ancient Iraq by Georges Roux — The definitive introduction to Mesopotamian history from the Sumerians to the Arab conquest. Dense but readable. Essential if you intend to visit the archaeological sites.
The Cultural Atlas of Mesopotamia and the Ancient Near East by Michael Roaf — A comprehensive, well-illustrated reference for the archaeology and history of the region.