The results of an investigation of the optical spectra of thirty-four emission nebulae in thirteen irregular and late-type spiral galaxies are presented. The program galaxies, with the number of nebulae observed in each shown in parentheses, were: NGC55 (3), IC1613 (2), NGC1156 (1), NGC1569 (3), NGC2366 (2), IC2574 (2), NGC4214 (3), NGC4236 (1), NGC4449 (4), NGC4656 (3), GR8 (1), NGC6822 (8), and IC5152 (1). Spectrophotometric data were gathered during 1978 and 1979 at the Cerro Tololo Interamerican Observatory (CTIO) using the SIT vidicon on the 4.0-m and 1.5-m telescopes, and at the Kitt Peak National Observatory (KPNO) using the Intensified Image Dissector Scanner (IIDS) on the 2.1-m telescope. From measurement of diagnostic emission-line strengths, the relative abundances of He, N, O, Ne, and S (in some cases) were calculated with respect to H for each nebula. Electron densities were derived from the ratio of the {S II} line intensities, I(6716)/I(6730), while temperatures were obtained from the ratio of the {O III} line intensities, I(4363)/I(5007). The observations reported in this work confirm the results of earlier investigations involving much smaller samples of irregular and late-type spiral galaxies; the galaxies examined during this study were found to be consistently underabundant in the metals with respect to earlier-type galaxies. The average abundances (by number) for all of the galaxies studied are: log(He) = 10.88, log(N) = 6.72, log(O) = 8.23, log(Ne) = 7.64, and log(S) = 7.20 (log(H) = 12.00). Interpretation of the abundances in the context of the closed-box model for galactic evolution provided yields of 5.9 x 10('-3), 9.5 x 10('-4), 3.2 x 10('-4), and 2.1 x 10('-3) for He, O, Ne, and Z respectively. These yields are consistent with an initial mass function of the form (theta) (PROPORTIONAL) (1/M)('(alpha)) with (alpha) in the range 7/3 to 10/3 for stars more massive than 10 M(,(CIRCLE)). In addition, a value for the primary yield of N of 2.5 x 10('-5) was determined. Examination of the metallicity parameter, Z, versus the astration parameter, ln(1/(mu)), suggests that the gassiest galaxies have experienced the least astrophysical processing. This result, coupled with a correlation that was found for Z versus log(total galaxy mass), suggests that the average star formation rate decreases as galaxy mass decreases. Finally, the pregalactic He abundance, by mass, was determined (Y(,p) = .216) and interpreted in the context of models of the standard big-bang. From this value of Y(,p) the present average density of the Universe is found to be 1.06 x 10('-31) g/cm('3)--insufficient to close the Universe.