We perform a comprehensive estimate of the frequency of galaxy mergers and their impact on star formation over z similar to 0.24-0.80 (lookback time T-b similar to 3-7 Gyr) using similar to 3600 (M >= 1 x 10(9) M-circle dot) galaxies with GEMS Hubble Space Telescope, COMBO-17, and Spitzer data. Our results are as follows. (1) Among similar to 790 high-mass (M >= 2.5 x 10(10) M-circle dot) galaxies, the visually based merger fraction over z similar to 0.24-0.80, ranges from 9% +/- 5% to 8% +/- 2%. Lower limits on the major merger and minor merger fraction over this interval range from 1.1% to 3.5%, and 3.6% to 7.5%, respectively. This is the first, albeit approximate, empirical estimate of the frequency of minor mergers over the last 7 Gyr. Assuming a visibility timescale of similar to 0.5 Gyr, it follows that over T-b similar to 3-7 Gyr, similar to 68% of high-mass systems have undergone a merger of mass ratio > 1/10, with similar to 16%, 45%, and 7% of these corresponding respectively to major, minor, and ambiguous "major or minor" mergers. The average merger rate is similar to a few x 10(-4) galaxies Gyr(-1) Mpc(-3). Among similar to 2840 blue-cloud galaxies of mass M >= 1.0 x 10(9) M-circle dot, similar results hold. (2) We compare the empirical merger fraction and merger rate for high-mass galaxies to three. cold dark matter-based models: halo occupation distribution models, semi-analytic models, and hydrodynamic SPH simulations. We find qualitative agreement between observations and models such that the (major+minor) merger fraction or rate from different models bracket the observations, and show a factor of 5 dispersion. Near-future improvements can now start to rule out certain merger scenarios. (3) Among similar to 3698 M >= 1.0 x 10(9) M-circle dot galaxies, we find that the mean star formation rate (SFR) of visibly merging systems is only modestly enhanced compared to non-interacting galaxies over z similar to 0.24-0.80. Visibly merging systems only account for a small fraction (< 30%) of the cosmic SFR density over T-b similar to 3-7 Gyr. This complements the results of Wolf et al. over a shorter time interval of T-b similar to 6.2-6.8 Gyr, and suggests that the behavior of the cosmic SFR density over the last 7 Gyr is predominantly shaped by non-interacting galaxies.