Both observations and simulations show that major tidal interactions or mergers between gas-rich galaxies can lead to intense bursts of star formation. Yet, the average enhancement in star formation rate (SFR) in major mergers and the contribution of such events to the cosmic SFR are not well estimated. Here we use photometric redshifts, stellar masses, and UV SFRs from COMBO-17, 24 mu m SFRs from Spitzer, and morphologies from two deep Hubble Space Telescope (HST) cosmological survey fields (ECDFS/GEMS and A901/STAGES) to study the enhancement in SFR as a function of projected galaxy separation. We apply two-point projected correlation function techniques, which we augment with morphologically selected very close pairs (separation <2 '') and merger remnants from the HST imaging. Our analysis confirms that the most intensely star-forming systems are indeed interacting or merging. Yet, for massive (M-* >= 10(10) M-circle dot) star-forming galaxies at 0.4 < z < 0.8, we find that the SFRs of galaxies undergoing a major interaction (mass ratios <= 1:4 and separations <= 40 kpc) are only 1.80 +/- 0.30 times higher than the SFRs of non-interacting galaxies when averaged over all interactions and all stages of the interaction, in good agreement with other observational works. Our results also agree with hydrodynamical simulations of galaxy interactions, which produce some mergers with large bursts of star formation on similar to 100 Myr timescales, but only a modest SFR enhancement when averaged over the entire merger timescale. We demonstrate that these results imply that only less than or similar to 10% of star formation at 0.4 <= z <= 0.8 is triggered directly by major mergers and interactions; these events are not important factors in the build-up of stellar mass since z = 1.