In cycling tissues that exhibit high turnover, tissue maintenance and repair are coordinated by stem cells. But, how frequently stem cells are replaced following differentiation, aging or injury remains unclear. By drawing together the results of recent lineage-tracing studies, we propose that tissue stem cells are routinely lost and replaced in a stochastic manner. We show that stem cell replacement leads to neutral competition between clones, resulting in two characteristic and recurring patterns of clone fate dynamics, which provide a unifying framework for interpreting clone fate data and for measuring rates of stem cell loss and replacement in vivo. Thus, we challenge the concept of the stem cell as an immortal, slow-cycling, asymmetrically dividing cell.