Substrate nanotopography affects cell adhesion and proliferation and is fundamental to the rational design of bio-adhesives, to tissue engineering and to the development of assays for in-vitro screening. Cell behavior on rough substrates is still elusive, and the results presented in the open literature remain controversial. Here, the proliferation of cells on electrochemically etched silicon substrates with different roughness and nearly similar surface energy was studied over three days with confocal and atomic force microscopy. The surface profile of the substrates is a self-affine fractal with a roughness R(a) growing with the etching time from approximately 2 to 100 nm and a fractal dimension D ranging between about 2 (nominally flat surface) and 2.6. For four cell types, the number of adhering cells and their proliferation rates exhibited a maximum on moderately rough (R(a) approximately 10-45 nm) nearly Brownian (D approximately 2.5) substrates. The observed cell behavior was satisfactorily interpreted within the theory of adhesion to randomly rough solids. These findings demonstrated the importance of nanogeometry in cell stable adhesion and growth, suggesting that moderately rough substrates with large fractal dimension could selectively boost cell proliferation.