Tracing molecular hydrogen content with carbon monoxide in low-metallicity galaxies has been exceedingly difficult. Here we present a new effort, with IRAM 30-m observations of 12 CO(1-0) of a sample of 8 dwarf galaxies having oxygen abundances ranging from 12 + log(O/H) ∼ 7.7 to 8.4. CO emission is detected in all galaxies, including the most metal-poor galaxy of our sample (0.1 Z ); to our knowledge this is the largest number of 12 CO(1-0) detections ever reported for galaxies with 12 + log(O/H) < ∼ 8 (0.2 Z ) outside the Local Group. We calculate stellar masses, M star , and star-formation rates (SFRs), and analyze our results in conjunction with galaxy samples from the literature. Extending previous results for a correlation of the molecular gas depletion time, τ dep , with M star and specific SFR (sSFR), we find a variation in τ dep of a factor of 200 or more (from < ∼ 50 Myr to ∼10 Gyr) over a spread of ∼10 3 in sSFR and M star . We exploit the variation of τ dep to constrain the CO-to-H 2 mass conversion factor α CO at low metallicity, and assuming a power-law variation find α CO ∝ Z/Z −2 , similar to results based on dust continuum measurements compared with gas mass. By including H I measurements, we show that the fraction of total gas mass relative to the baryonic mass is higher in galaxies that are metal poor, of low mass, and with high sSFR. Finally, comparisons of the data with star-formation models of the molecular gas phases show that the models are generally quite successful, but at metallicities Z/Z < ∼ 0.2, there are some discrepancies.