A couple years ago, I got tired of running across repeated references to books I hadn't read, references that indicated that these books were fundamental to understanding the topic, or at least to the discussion. So I started following up on the references and actually reading the "canon" for the subjects I read regularly: The Death and Life of Great American Cities, The Frontier in American History, The Feminine Mystique, and most recently, Democracy in America. Not all of these have been easy reading, but they are all interesting and thought-provoking (which is undoubtedly why they are referred to so often).
Democracy in America, Vol. 1, is the best book I've read for understanding how the US still works, even if it was written in 1833. The insights into the democracy of the period are interesting historically, but they are also helpful for understanding what has happened since then, both in the US and internationally. The US is still substantially the way Tocqueville describes it, and the changes are generally extensions of the characteristics he noted or predicted. I sometimes found it hard to follow the distinctions he makes between various forms of governing (legislative vs. executive; governors as magistrates) but trying was enlightening - I had never made the distinctions before.
The main difference between the 1830s and now is that the Federal government was weak and the individual states strong; people looked first to the state to exercise power while the Federal government mostly mediated between the states, and its influence on citizens was generally exercised via the states. Over time, as population mobility increased and local attachments faded, as interstate commerce expanded dramatically, the Federal government gained strength; it now controls a vastly greater portion of daily life than Tocqueville foresaw and is much stronger. Part of this may be a result of the Civil War, which Tocqueville predicted; but he felt that the union would disintegrate under the strong action of the states, rather than holding together and subduing them. For reasons that probably turn on leadership, the union didn't come apart, and the United States of America made the transition from a plural noun and idea ("The United States are...") to a singular one ("The United States is..."), from a federation of mostly sovereign states to a unified country. The Civil War wasn't just a sibling fight, it was a turning point in the evolving concept of the country.