Central to the classical hematopoietic stem cell (HSC) paradigm is the concept that the maintenance of blood cell numbers is exclusively executed by a discrete physical entity: the transplantable HSC. The HSC paradigm has served as a stereotypic template in stem cell biology, yet the search for rare, hardwired professional stem cells has remained futile in most other tissues. In a more open approach, the focus on the search for stem cells as a physical entity may need to be replaced by the search for stem cell function, operationally defined as the ability of an organ to replace lost cells. The nature of such a cell may be different under steady state conditions and during tissue repair. We discuss emerging examples including the renewal strategies of the skin, gut epithelium, liver, lung, and mammary gland in comparison with those of the hematopoietic system. While certain key housekeeping and developmental signaling pathways are shared between different stem cell systems, there may be no general, deeper principles underlying the renewal mechanisms of the various individual tissues.