The majority of atomic hydrogen Br Delta *g emission detected in the spectra of young stellar objects is believed to arise from the recombination regions associated with the magnetospheric accretion of circumstellar disk material onto the forming star. In this paper, we present the results of a K-band integral field unit spectroscopic study of Br Delta *g emission in eight young protostars: CW Tau, DG Tau, Haro 6-10, HL Tau, HV Tau C, RW Aur, T Tau, and XZ Tau. We spatially resolve Br Delta *g emission structures in half of these young stars and find that most of the extended emission is consistent with the location and velocities of the known Herbig-Haro flows associated with these systems. At some velocities through the Br Delta *g line profile, the spatially extended emission comprises 20% or more of the integrated flux in that spectral channel. However, the total spatially extended Br Delta *g is typically less than ~10% of the flux integrated over the full emission profile. For DG Tau and Haro 6-10 S, we estimate the mass outflow rate using simple assumptions about the hydrogen emission region and compare this to the derived mass accretion rate. We detect extended Br Delta *g in the vicinity of the more obscured targets in our sample and conclude that spatially extended Br Delta *g emission may exist toward other stars, but unattenuated photospheric flux probably limits its detectability.