The ability of reptation theories to quantitatively predict the linear viscoelastic response of linear polymer melts is systematically tested for various combinations of almost monodisperse, bidisperse, and polydisperse polystyrene (PS), high-density polyethylene (PE), and polycarbonate (PC) samples. Broad industrial HDPE and PC samples have been fractionated according to molar weight by preparative methods. The experimental master curves for dynamic moduli G' and G" are compared with predictions obtained from the experimentally determined molecular weight distribution (MWD) (by size exclusion chromatography) with the help of reptation models proposed in the literature. We focus on the Doi and Edwards relaxation function, with and without fluctuation effects, and the des Cloizeaux time-dependent diffusion relaxation function. These relaxation functions are combined with double reptation. We conclude that the des Cloizeaux relaxation function, associated with the double reptation model, gives the best results for well-entangled polymers, which are in quantitative agreement with experimental data. Indeed, it is the only model that is able to correctly predict the intermediate region between reptation relaxation and Rouse relaxation. We study the influence of short chains (slightly longer than the critical molecular weight) on the relaxation moduli of blends with long chains. We conclude that the model predicts that the chains smaller than 4M(e) relax too quickly in comparison with the experimental data. After a modification of the model, quantitative predictions are also obtained.