The high opacity of He I λ10830 makes it an exceptionally sensitive probe of the inner wind geometry of accreting T Tauri stars. In this line, blueshifted absorption below the continuum results from simple scattering of stellar photons, a situation that is readily modeled without definite knowledge of the physical conditions and recourse to multilevel radiative transfer. We present theoretical line profiles for scattering in two possible wind geometries, a disk wind and a wind emerging radially from the star, and compare them to observed He I λ10830 profiles from a survey of classical T Tauri stars. The comparison indicates that subcontinuum blueshifted absorption is characteristic of disk winds in ∼30% of the stars and of stellar winds in ∼40%. We further conclude that for many stars the emission profile of helium likely arises in stellar winds, increasing the fraction of accreting stars inferred to have accretion-powered stellar winds to ∼60%. Stars with the highest disk accretion rates are more likely to have stellar wind than disk wind signatures and less likely to have redshifted absorption from magnetospheric funnel flows. This suggests the possibility that when accretion rates are high, disks can extend closer to the star, magnetospheric accretion zones can be reduced in size, and conditions can arise that favor radially outflowing stellar winds.