A number of instruments have been designed to probe the variety of attitudes, beliefs, expectations, and epistemological frames taught in our introductory physics courses. Using a newly developed instrument -- the Colorado Learning Attitudes about Science Survey (CLASS) -- we examine the relationship between students' beliefs about physics and other educational outcomes, such as conceptual learning and student retention. We report results from surveys of over 750 students in a variety of courses, including several courses modified to promote favorable beliefs about physics. We find positive correlations between particular student beliefs and conceptual learning gains, and between student retention and favorable beliefs in select categories. We also note the influence of teaching practices on student beliefs.