Soft polymer networks with large mesh size, not flat rigid surfaces, are the normal environment for most animal cells. Cell structure and function depend on the stiffness of the surfaces on which cells adhere as well as on the type of adhesion complex by which the cell binds its extracellular ligand. Many cell types, including fibroblasts and endothelial cells, switch from a round to spread morphology as stiffness is increased between 1000 and 10,000 Pa. Coincident with the change in morphology are a host of differences in protein phosphorylation levels, expression of integrins, and changes in cytoskeletal protein expression and assembly. In contrast, other cells types such as neutrophils and platelets do not require rigid substrates in order to spread, and neurons extend processes better on soft (50 Pa) materials than on stiffer gels. We compare the stiffness sensing of four cell types: platelets, neurons and astrocytes, a glial cell type derived from embryonic rat brain, and melanoma cells. Astrocytes switch from a round to spread morphology as substrate stiffness increases, but do so over a stiffness range 10 times softer than that over which fibroblasts alter morphology. Stiffness-dependent morphologic changes observed from studies of cells grown on surfaces of protein-laminated polyacrylamide gels that have linear elasticity are also seen when cells are on matrices of natural biopolymers such as fibrin. Biopolymer gels like fibrin can be formed with appropriate stiffness to optimize for neuronal cell survival and patterning, and may have utility for repair of damaged neural tissues. The complex non-linear rheology of fibrin and other gels formed by semi-flexible biopolymers that exhibit strain-stiffening provide additional mechanisms by which cells can respond to and actively remodel the mechanical features of their environment.