This article considers some of the practical problems inherent in interim analyses and stopping rules for randomized clinical trials. Topics covered include group sequential designs, trials with unplanned interim analyses, estimation problems in clinical trials with planned interim analyses, and the balance between individual and collective ethics. Particular attention is paid to the fact that clinical trials that stop early are prone to exaggerate the magnitude of treatment effect. Accordingly, a Bayesian "shrinkage" method of analysis is proposed to help quantify the extent to which surprisingly large point and interval estimates of treatment difference in clinical trials that stop early should be moderated.