Unlike traditional approaches, Bayesian methods enable formal combination of expert opinion and objective information into interim and final analyses of clinical trial data. However, most previous Bayesian approaches have based the stopping decision on the posterior probability content of one or more regions of the parameter space, thus implicitly determining a loss and decision structure. In this paper, we offer a fully Bayesian approach to this problem, specifying not only the likelihood and prior distributions but appropriate loss functions as well. At each data monitoring point, we enumerate the available decisions and investigate the use of backward induction, implemented via Monte Carlo methods, to choose the optimal course of action. We then present a forward sampling algorithm that substantially eases the analytic and computational burdens associated with backward induction, offering the possibility of fully Bayesian optimal sequential monitoring for previously untenable numbers of interim looks. We show that forward sampling can always identify the optimal sequential strategy in the case of a one-parameter exponential family with a conjugate prior and monotone loss functions as well as the best member of a certain class of strategies when backward induction is infeasible. Finally, we illustrate and compare the forward and backward approaches using data from a recent AIDS clinical trial.