It is difficult to measure teaching quality at the postsecondary level because students typically "self-select" their coursework and their professors. Despite this, student evaluations of professors are widely used in faculty promotion and tenure decisions. We exploit the random assignment of college students to professors in a large body of required coursework to examine how professor quality affects student achievement. Introductory course professors significantly affect student achievement in contemporaneous and follow-on related courses, but the effects are quite heterogeneous across subjects. Students of professors who as a group perform well in the initial mathematics course perform significantly worse in follow-on related math, science, and engineering courses. We find that the academic rank, teaching experience, and terminal degree status of mathematics and science professors are negatively correlated with contemporaneous student achievement, but positively related to follow-on course achievement. Across all subjects, student evaluations of professors are positive predictors of contemporaneous course achievement, but are poor predictors of follow-on course achievement.