We investigate how the different types of supernovae are relatively affected by the metallicity of their host galaxy. We match the SAI Supernova Catalog to the SDSS-DR4 catalog of star-forming galaxies with measured metallicities. These supernova host galaxies span a range of oxygen abundance from 12 + log(O/H) = 7.9 to 9.3 (~ 0.1 to 2.7 solar) and a range in absolute magnitude from MB = -15.2 to -22.2. To reduce the various observational biases, we select a subsample of well-characterized supernovae in the redshift range from 0.01 to 0.04, which leaves us with 58 SN II, 19 Ib/c, and 38 Ia. We find strong evidence that SN Ib/c are occurring in higher-metallicity host galaxies than SN II, while we see no effect for SN Ia relative to SN II. We note some extreme and interesting supernova-host pairs, including the metal-poor (~ 1/4 solar) host of the recent SN Ia 2007bk, where the supernova was found well outside of this dwarf galaxy. To extend the luminosity range of supernova hosts to even fainter galaxies, we also match all the historical supernovae with z < 0.3 to the SDSS-DR6 sky images, resulting in 1225 matches. This allows us to identify some even more extreme cases, such as the recent SN Ic 2007bg, where the likely host of this hypernova-like event has an absolute magnitude MB ~ -12, making it one of the least-luminous supernova hosts ever observed. This low-luminosity host is certain to be very metal poor (~ 1/20 solar), and therefore this supernova is an excellent candidate for association with an off-axis GRB. The two catalogs that we have constructed are available online and will be updated regularly. Finally, we discuss various implications of our findings for understanding supernova progenitors and their host galaxies.