Cancer is the second leading cause of death in the United States. Cancer incidence and mortality rates measure the progress against cancer; these rates are obtained from the Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute (NCI). Lung cancer has the highest mortality rate among all cancers, whereas prostate cancer has the highest number of new cases among males. In this article, we analyze the incidence rates of these two cancers, as well as colon and rectal cancer. The NCI reports trends in cancer age-adjusted mortality and incidence rates in its annual report to the nation and analyzes them using the Joinpoint software. The location of the joinpoints signifies changes in cancer trends, whereas changes in the regression slope measure the degree of change. The Joinpoint software uses a numerical search to detect the joinpoints, fits regression within two consecutive joinpoints by least squares, and finally selects the number of joinpoints by either a series of permutation tests or the Bayesian information criterion. We propose Bayesian joinpoint models and provide statistical estimates of the joinpoints and the regression slopes. While the Joinpoint software and other work in this area assumes that the joinpoints occur on the discrete time grid, we allow a continuous prior for the joinpoints induced by the Dirichlet distribution on the spacings in between. This prior further allows the user to impose prespecified minimum gaps in between two consecutive joinpoints. We develop parametric as well as semiparametric Bayesian joinpoint models; the semiparametric framework relaxes parametric distributional assumptions by modeling the distribution of regression slopes and error variances using Dirichlet process mixtures. These Bayesian models provide statistical inference with finite sample validity. Through a simulation study, we demonstrate the performance of the proposed parametric and semiparametric joinpoint models and compare the results with the ones from the Joinpoint software. We analyze age-adjusted cancer incidence rates from the SEER Program using these Bayesian models with different numbers of joinpoints by employing the deviance information criterion and the cross-validated predictive criterion. In addition, we model the lung cancer incidence rates and the smoking rates jointly and explore the relation between the two longitudinal processes.