We apply fast field cycling NMR to study the dispersion of the H-1 spin-lattice relaxation time T-1(omega) of linear 1,4-polybutadienes with molecular weight M (g/mol) ranging from M = 355 to 817 000. By this, the crossover from glassy dynamics through Rouse to reptation becomes accessible. Analyzing the data in the susceptibility form omega/T-1(omega) and applying frequency-temperature superposition, spectra extending over up to 8 decades in omega are obtained. Characteristic polymer spectra are revealed when the underlying glassy dynamics are accounted for. Instead of describing the unentangled melt by the full Rouse mode spectrum, the emergence of a limited number of modes is identified which saturates when entanglement sets in. A quantitative analysis yields the molecular weight of a Rouse unit M-R congruent to 500, and the entanglement weight M-e congruent to 2000, at which first entanglement effects are observed. Moreover, the dynamic order parameter S(M) and the behavior of the terminal time T-max(M) are obtained. Both quantities allow to identify three dynamic regimes, namely simple liquid, Rouse, and reptation dynamics. The temperature dependence of the segmental relaxation time tau(s)(T) coincides with the corresponding dielectric relaxation times which were measured additionally, and the M dependence of the glass transition temperature T, shows distinctive kinks at M-R and M-e, indicating that glassy dynamics are modified by polymer dynamics.