We have used the Hubble Space Telescope to image two regions of the Orion Nebula in low and high ionization emission lines. There appear to be two systems of Herbig-Haro objects in the Orion nebula - a ``North'' System is centered slightly north of the BN and IRc2 sources, and a ``South'' System is centered south of the Trapezium stars. The North System appears to be the result of shocks on the near side of OMC-1, the host molecular cloud for M42. The sources of these HH objects are most likely to be instabilities in shocks driven by massive star winds penetrating into a region of decreasing ambient density. HH 201 displays many of the observed characteristics of the North System members but lacks a trailing H2 finger. HH208 and 209 share this latter property and also display a very different morphological form, which puts their association with the North System in doubt. The South System contains large shocks with a variety of morphologies. This system is most likely a combination of shocks in the ionized nebular gas and lower ionization shocks formed when jets from low mass young stars strike the neutral lid lying on the near side of M42. Both shocks and photoionization affect the line excitation of HH objects in M42, especially among the South System, where ultraviolet light from Theta1C Ori penetrates into the back side of a bow shock that moves toward the observer. Among the bow-shaped objects along the fingers in the North system, the highest excitation lines occur near the apices of the bows, as predicted by theory. Objects that lie closer to the Trapezium are more difficult to analyze because of stronger nebular emission, rendering the HH objects best visible in [O I] and [S II] emission.