We experimentally demonstrate the direct measurement of net group and reshaping delays for arbitrary optical pulses in dispersive media, verifying the earlier prediction of Peatross et al. [Phys. Rev. Lett. 84, 2370 (2000)]. Incoherent pulse propagation in an absorptionless system is well described by net group delay; even the medium causes a great deal of deformation in the transmitted pulse. However, in the case of phase modulated chirping pulses in a resonant absorber, the so-called superluminal or subluminal propagation velocity is strongly influenced by the reshaping delay.