Especially The Growth of the American Republic (with Samuel Eliot Morison, New York: Oxford University Press, 1930 [as Oxford History of the United States; 7th ed., 1980.]. Revised and abridged edition with Samuel Eliot Morison and William E. Leuchtenberg published by Oxford University Press in 1980 as Concise History of the American Republic, rev. 1983.
Documents of American History (1934 et al.)
Readings in American History (with Allan Nevins, 1939)
Extremely worthwhile: The American Mind: An Interpretation of American Thought and Character Since the 1880s (1950)
Also crucial: The Empire of Reason: How Europe Imagined and America Realized the Enlightenment (Garden City, NY: Anchor Press / Doubleday, 1977, and later reprintings.)
Commager on Tocqueville (Columbia: University of Missouri Press, 1993): best discussion of Alexis de Tocqueville, French author and political scholar who travelled extensively in the US in the early 19th Century. http://en.wikipedia.org/wiki/Alexis_de_Tocqueville