The prevailing stem cell concept is derived from the large body of evidence available on the structure of the blood-generating system. Hemopoiesis is organized such that a multipotent stem cell, endowed with self-renewal capacity, is viewed as being positioned at the origin of a hierarchical tree of branching specificities, increasing maturity and decreasing self-renewal ability. Data accumulated in recent years on various stem cell systems often contradict this traditional view of stem cells and are reviewed herein. It is suggested that other options should be considered and put to experimental scrutiny; it is argued that the organization of the hemopoietic system may not represent a general structure of stem cell systems. The basic trait of the stem state is proposed to be plasticity. Self-renewal is not a specific stem cell trait; rather, it is exhibited by some mature cell types, whereas other particular stem cells are endowed with relatively poor renewal ability. Hierarchical structuring is also proposed to be an optional stem cell trait and may exist only in specific tissues where it serves the need for rapid expansion. The stem state is therefore defined by the highest degree of plasticity of a cell, within the repertoire of cell types present in the organism.