Absorption, gain, and luminescence spectra of quasi-two-dimensional electron-hole plasmas in semiconductor quantum-well structures are calculated as functions of the plasma density and temperature. Self-energy corrections and the effects of multiple electron-hole scattering are evaluated for a statically screened Coulomb interaction. The Bethe-Salpeter equation for the electron-hole pair propagator is solved both numerically and analytically using a method developed by Noyes. The resulting spectra deviate considerably from the corresponding free-particle spectra, due to the strong pair fluctuations in two dimensions. Implications for the theory of quantum-well lasers are discussed.