Improved calculations of X-ray spectra for supernova remnants (SNRs) in the Sedov-Taylor phase are reported, which for the first time include reliable atomic data for Fe L-shell lines. This new set of Sedov models also allows for a partial collisionless heating of electrons at the blast wave and for energy transfer from ions to electrons through Coulomb collisions. X-ray emission calculations are based on the updated Hamilton-Sarazin spectral model. The calculated X-ray spectra are successfully interpreted in terms of three distribution functions: the electron temperature and ionization timescale distributions, and the ionization timescale-averaged electron temperature distribution. The comparison of Sedov models with a frequently used single nonequilibrium ionization (NEI) timescale model reveals that this simple model is generally not an appropriate approximation to X-ray spectra of SNRs. We find instead that plane-parallel shocks provide a useful approximation to X-ray spectra of SNRs, particularly for young SNRs. Sedov X-ray models described here, together with simpler plane shock and single-ionization timescale models, have been implemented as standard models in the widely used XSPEC v11 spectral software package.