We have determined parameters and abundances for three SMC and nine LMC Cepheids that have not been previously studied spectroscopically for metallicity, as well as three SMC and one LMC Cepheids observed previously by Luck & Lambert. This work nearly doubles the number of Cepheids with spectroscopic metallicities in the SMC and triples the number in the LMC. For Galactic reference stars we have determined the abundances of 11 supergiants of spectral type F0 to K1. These abundances are used herein to examine the dispersion in cosmic [Fe/H] values found in LMC Cepheids by Luck & Lambert, and in later papers will be used to correct the distance moduli obtained by us for these Cepheids using the visual surface brightness technique. The Magellanic Cloud Cepheids tend to be longer-period Cepheids (the period range examined was from 37 to 133 days), and thus have physical gravities (derived from the period-luminosity relation and an inferred mass) that are 1.0 dex and lower. Spectroscopic gravities (derived by forcing the total Fe content, as determined from Fe I and Fe II, to be equal) are even lower. Fortunately, the [Fe/H] content as determined from Fe I is not strongly dependent on gravity and is thus well determined. We combine our abundances with other published high-resolution spectroscopic results, deriving a mean [Fe/H] for the SMC of -0.68 (σ = 0.13, n = 25). The total range seen in the [Fe/H] ratios derived herein is -0.84 to -0.65. This result is in agreement with previous studies showing a small intrinsic range in the metallicities in the SMC. For the LMC, from the Cepheids studied here we obtain -0.30 (σ = 0.12, n = 10), with a range of -0.55 to -0.19. Combining all available data, we obtain a mean [Fe/H] of -0.34 (σ = 0.15, n = 32). From this analysis, there is little evidence for a significant metallicity dispersion in the LMC.