We present an atlas of three-dimensional (position-position-velocity) spectra of the Orion Nebula in optical emission lines from a variety of different ionization stages: [O I] 6300, [S II] 6716,6731, [N II] 6584, [S III] 6312, H alpha 6563, and [O III] 5007. These transitions provide point to point information about the physical structure and kinematics of the nebula at an effective resolution of 3 x 2 x 10 km/s, clearly showing the large scale behavior of the ionized gas and the presence of localized phenomena such as Herbig-Haro outflows. As an example application of the atlas, we present a statistical analysis of the widths of the H alpha, [O III], and [N II] lines that permits a determination of the mean electron temperature in the nebula of (9200 +/- 400) K. We also find, in contradiction to previous claims, that the non-thermal line broadening is not significantly different between recombination lines and collisional lines.