After much reflection, I think I can add two more books to my "most influential" list, bringing me to my quota.
Mathematical Optimization and Economic Theory, Michael Intiligator. This fantastically lucid book taught me micro in grad school, helping me see (although this is nowhere mentioned in the book itself) that the math embodies a precise social theory. (Or, to be more exact, a pre-social theory.)
Atlantic Crossings: Social Politics in a Progressive Age, Daniel Rodgers. This is spectacularly well-written, but its main impact has been to alter my thinking about "reform" by seeing familiar issues in broad historical perspective. Also, the lives of reformers themselves often seem to trace a similar arc.