We present ultraviolet through near-infrared photometry and spectroscopy of the host galaxies of all superluminous supernovae (SLSNe) discovered by the Palomar Transient Factory prior to 2013 and derive measurements of their luminosities, star formation rates, stellar masses, and gas-phase metallicities. We find that Type I (hydrogen-poor) SLSNe (SLSNe I) are found almost exclusively in low-mass (M_*_<2x10^9^M_{sun}_) and metal-poor (12+log_10_[O/H]<8.4) galaxies. We compare the mass and metallicity distributions of our sample to nearby galaxy catalogs in detail and conclude that the rate of SLSNe I as a fraction of all SNe is heavily suppressed in galaxies with metallicities >~0.5Z_{sun}_. Extremely low metallicities are not required and indeed provide no further increase in the relative SLSN rate. Several SLSN I hosts are undergoing vigorous starbursts, but this may simply be a side effect of metallicity dependence: dwarf galaxies tend to have bursty star formation histories. Type II (hydrogen-rich) SLSNe (SLSNe II) are found over the entire range of galaxy masses and metallicities, and their integrated properties do not suggest a strong preference for (or against) low-mass/low-metallicity galaxies. Two hosts exhibit unusual properties: PTF 10uhf is an SLSN I in a massive, luminous infrared galaxy at redshift z=0.29, while PTF 10tpz is an SLSN II located in the nucleus of an early-type host at z=0.04.