We present near-infrared K-band spectra for a sample of 7 Class 0 protostars in the Perseus and Orion star-forming regions. We detect Br gamma, CO overtone, and H2 emission, features that probe the near circumstellar environment of the protostar and reveal evidence of magnetospheric accretion, a hot inner disk atmosphere, and outflows, respectively. Comparing the properties of these features with those of Class I sources from the literature, we find that their Br gamma and CO emission are generally consistent in strength and velocity width. The Br gamma line profiles are broad and centrally peaked, with FWHMs of 200 km/s and wings extending to 300 km/s. The line ratios of our H2 emission features, which are spatially extended for some sources, are consistent with shock excitation and indicate the presence of strong jets or a disk wind. Within our small sample, the frequency of CO band emission (67%) is high relative to that of Class I samples (15%), indicating that Class 0s have high inner disk accretion rates, similar to those of the most actively accreting Class I sources. Collectively, our results suggest that Class 0 sources have similar accretion mechanisms to the more evolved classes, with strong organized stellar magnetic fields established at the earliest observable stage of evolution.