Craig graduated in history from Princeton University, was a Rhodes Scholar at Balliol College, Oxford, from 1936 to 1938, and served in the U.S. Marine Corps as a captain and in the Office of Strategic Services during World War II. In 1941, he co-edited with Edward Mead Earle and Felix Gilbert, on behalf of the American War Department, the book Makers of Modern Strategy: Military Thought From Machiavelli to Hitler, which was intended to serve as a guide to strategic thinking for military leaders during the war.

After 1945, Craig worked as a consultant to the U.S. Arms Control and Disarmament Agency, the State Department, the U.S. Air Force Academy and the Historical Division of the U.S. Marine Corps. He was a professor at Princeton University from 1950-61 and at Stanford University from 1961-79. In 1956-1957, he taught at the Center for Advanced Study in the Behavioral Sciences. In addition, he often held visiting professorships at the Free University of Berlin; in 1967, Craig was the only professor there to sign a petition asking for an investigation into charges of police brutality towards protesting students. Craig was chair of the history department at Stanford in 1972-1975 and 1978-1979. Between 1975-1985, he served as the vice-president of the Comité International des Sciences Historiques. In 1979, he became an emeritus professor and was awarded the title J. E. Wallace Sterling Professor of Humanities.

During his time at Stanford, Craig was considered to be a popular and innovative teacher who improved both undergraduate and graduate teaching, while remaining well-liked by the students. After his retirement, he worked as a book reviewer for the New York Review of Books. Some of his reviews attracted controversy, most notably in April 1996, when he praised Daniel Goldhagen's book Hitler's Willing Executioners and later in September of the same year when he argued that David Irving's work was valuable because of what Craig saw as Irving's devil's advocate role. Craig argued that Irving was usually wrong, but that by promoting what Craig saw as a twisted and wrongheaded view of history with a great deal of élan, Irving forced other historians to fruitfully examine their beliefs about what is known about the Third Reich.

Craig was formerly President of the American Historical Association. In 1953, together with his friend Felix Gilbert, he edited a prosopography of inter-war diplomats entitled The Diplomats, an important source for diplomatic history in the interwar period. He followed this book with studies on the Prussian Army, the Battle of Königgrätz and many aspects of European and German history. Craig was particularly noted for his contribution to the Oxford History of Modern Europe series entitled Germany, 1866-1945 and its companion volume, The Germans. The latter was a wide-ranging cultural history that explored aspects of being German, such as attitudes towards German-Jewish relations, money, students, women, and democracy, amongst others. The book was a best-seller in both the United States and Germany and Craig was awarded the Pour le Mérite medal for this book. Increasingly interested in cultural history in his later years, Craig subsequently wrote studies of several German writers, most notably Theodor Fontane. During this time, he also emerged as a celebrity in the German-speaking world, frequently appearing as a guest on German television talk shows. By his later years, Craig was widely regarded as the doyen of American historians of Germany, and his opinions carried much weight.

Craig died in 2005, and was survived by his widow Phyllis, four children and eight grandchildren.