Many experimental findings on heterogeneity, flexibility, and plasticity of tissue stem cells are currently challenging stem cell concepts that assume a cell intrinsically predefined, unidirectional differentiation program. In contrast to these classical concepts, nonhierarchical self-organizing systems provide an elegant and comprehensive alternative to explain the experimental data. Here we present the application of such a self-organizing concept to quantitatively describe the hematopoietic stem cell system. Focusing on the analysis of individual-stem-cell fates and clonal dynamics, we particularly discuss implications of the theoretical results on the interpretation of experimental findings. We demonstrate that it is possible to understand hematopoietic stem cell organization without assumptions on unidirectional developmental hierarchies, preprogrammed asymmetric division events or other assumptions implying the existence of a predetermined stem cell entity. The proposed perspective, therefore, changes the general paradigm of thinking about stem cells.