Generation of directional movement at the molecular scale is a phenomenon crucial for biological organization and dynamics. It is traditionally described in mechanistic terms, in consistency with the conventional machine-like image of the cell. The designated and highly specialized protein machines and molecular motors are presumed to bring about most of cellular motion. A review of experimental data suggests, however, that uncritical adherence to mechanistic interpretations may limit the ability of researchers to comprehend and model biology. Specifically, this article illustrates that the interpretation of molecular motors and protein translocation in terms of stochasticity and self-organization appears to provide a more adequate and fruitful conceptual framework for understanding of biological organization at the molecular scale.