  Electronic and optical properties of materials are affected by atomic motion
through the electron-phonon interaction: not only band gaps change with
temperature, but even at absolute zero temperature, zero-point motion causes
band-gap renormalization. We present a large-scale first-principles evaluation
of the zero-point renormalization of band edges beyond the adiabatic
approximation. For materials with light elements, the band gap renormalization
is often larger than 0.3 eV, and up to 0.7 eV. This effect cannot be ignored if
accurate band gaps are sought. For infrared-active materials, global agreement
with available experimental data is obtained only when non-adiabatic effects
are taken into account. They even dominate zero-point renormalization for many
materials, as shown by a generalized Fr\"ohlich model that includes multiple
phonon branches, anisotropic and degenerate electronic extrema, whose range of
validity is established by comparison with first-principles results.
