The time-of-flight technique was used with the "ring" scattering geometry in a laboratory with low neutron-scattering background to measure the angular distributions of the cross sections for elastic and inelastic scattering of 14-MeV neutrons in natural chromium, iron, nickel, and niobium. Specifically for inelastic scattering, the measurements included the 1.43- and 4.56-MeV levels of 52Cr; the 0.85-, (2.94 to 3.12)-, and (4.46 to 4.51)-MeV level groups of 56Fe; the 1.33-MeV level of 60Ni combined with the 1.45-MeV level of 58Ni; and the 4.48-MeV level of 58Ni. Pulses of neutrons with time width of 0.9 to 1.1 ns were produced via the D-T reaction in a 150-keV linear accelerator, with average intensities of 9 × 108 n/s. The scattering angles ranged from ~16 to ~160 deg, with a typical step of ~10 deg. The overall uncertainty for the elastic scattering cross section was in the range of 7 to 10% for all materials, except around the minima of the angular distribution for niobium. The uncertainties for the inelastic scattering cross sections were estimated to be between 8 and 24%. The measured angular distributions were compared with the evaluations in the ENDF/B-VI, JENDL-3, CENDL-2, BROND-2, and JEF-2 nuclear data libraries. For elastic scattering, there are no significant discrepancies in general, neither among the evaluations nor between the present data and the evaluations. For the inelastic scattering there are substantial discrepancies both in shape and magnitude among the evaluations (when available) as well as between the present data and the evaluations.