Spherically averaged electron momentum densities Pi(p) are constructed by the numerical Hartree-Fock method for all 103 atoms from hydrogen (atomic number Z = 1) to lawrencium (Z = 103) in their experimental ground states, We find three different types of momentum densities spread across the periodic table in a very simple manner for the 98 atoms other than He, N, Mn, Ge, and Pd. Atoms in groups 1-6, 13, and 14, and all lanthanides and actinides have a unimodal momentum density with a maximum at p = 0, atoms in groups 15-18 have a unimodal momentum density with a local minimum at p = 0 and a maximum at p > 0, and atoms in groups 7-12 have a bimodal momentum density with a primary maximum at p = 0 and a small secondary maximum at p > 0. Our. results confirm the existence of nonmonotonic momentum densities reported in the literature, but also reveal some errors in the previous classification of atomic momentum densities. The:physical origin for the appearance of the three different modalities in Pi(p) is clarified by analysis of subshell contributions to momentum densities.