The electronic structure of few-layer graphene (FLG) samples with crystalline order was investigated experimentally by infrared absorption spectroscopy for photon energies ranging from 0.2-1 eV. Distinct optical conductivity spectra were observed for different samples having precisely the same number of layers. The different spectra arise from the existence of two stable polytypes of FLG, namely, Bernal (AB) stacking and rhombohedral (ABC) stacking. The observed absorption features, reflecting the underlying symmetry of the two polytypes and the nature of the associated van Hone singularities, were reproduced by explicit calculations within a tight-binding model. The findings demonstrate the pronounced effect of stacking order on the electronic structure of FLG.