The Monkey Cage's guest-poster Colin Moore points to John Judis' "Ten Books Any Student of American History Must Read" (descriptive links to each are included in Judis' New Republic piece): Perry Miller, Errand into the Wilderness; William McLoughlin, Revivals, Awakenings and Reform; Gordon Wood, The Creation of the American Republic, 1776-1787; Michael Paul Rogin, Fathers and Children: Andrew Jackson and the Subjugation of the American Indian; Herbert Croly, The Promise of American Life; Martin J. Sklar, The Corporate Reconstruction of American Capitalism, 1890-1916; Warren Susman, Culture and History; Harold Cruse, The Crisis of the Negro Intellectual; William Appleman Williams, The Contours of American History; and Louis Hartz, The Liberal Tradition in America.
Among those works I'm familiar with, I'd most recommend Hartz's Liberal Tradition, but that mostly reflects a personal prejudice: my fondness for postwar American historiography, known as the "consensus" school (as opposed to "conflict" as America's running theme, which, historiographically, followed in the 1960s and beyond).
Moore adds five others: Richard White, The Middle Ground; Bernard Bailyn, The Ideological Origins of the American Revolution; W.E.B. DuBois, Black Reconstruction in America; Theda Skocpol, Protecting Soldiers and Mothers; and Richard Hofstadter, Anti-Intellectualism in American Life.
Anything by Bailyn is extraordinary, and Skocpol's volume is simply masterful, plus it comes with an enchanting historical dig at Republicans: It was you guys, and not Democrats, who launched the vote-buying welfare state by passing out Civil War pensions like cheap whisky.
But if you're just introducing yourself to professional political history, read, above all others, Richard Hofstadter (you know, the "paranoid style" dude). Anti-Intellectualism is, like everything he wrote, excellent, however I'd first recommend his American Political Tradition or The Age of Reform. Hofstadter knew not only how to write history, he knew how to write. He was smooth, droll, contemplative, original, and more journalistic than--egads--academic.
He's an unending pleasure, as well as, in my opinion, the greatest.