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We have observed 10 hydrocarbon species at 3 mm wavelength in three translucent clouds and in TMC-1 and L183. The 10 species are C₂H, c-C₃H, l-C₃H, c-C₃H₂, l-C₃H₂, CH₃CCH, C₄H, C₄H₂, C₅H, and C₆H, where c- and l- designate the cyclical and linear isomers. Abundances for these, as well as the previously observed species CH₃C₄H and C₆H₂, have been derived from statistical equilibrium analyses. These species are key members of the hydrocarbon network–the ``backbone'' of gas-phase interstellar chemistry, from which most species containing N, O, and C atoms stem directly. All of the observed hydrocarbon species except c-C<sub>3</sub>H and c-C<sub>3</sub>H<sub>2</sub> are ``chain''-type molecules or have a linear-chain isomer. The latter species are known to have stable cyclic isomers as well. We observe large c-/l-abundance ratios for C₃H₂, especially in the dark clouds, that can be explained under steady state conditions by existing knowledge of the chemistry. We also observe ortho/para ratios for c- and l-C₃H₂, and for C₄H₂, that exceed the high-temperature limit in nearly every case, often by large factors. O/P ratios as large as ∼5 can be explained by protonation via H⁺₃. By contrast, E/A ratios are observed to be less than the high-T limit for all three C_3v species (CH₃C₂H, CH₃C₄H, CH₃CN), because H⁺₃ protonation is not possible. The New Standard Chemistry model (Lee et al.) has been modified to accommodate several cyclical and chain-type hydrocarbon species. In addition to the large c-/l- and O/P ratios, we find very good agreement between model predictions and observed total abundances for all 12 species under steady state conditions. Early-time chemistry is not required but cannot be ruled out. It easily produces the very large c-C₃H₂/l-C₃H₂ ratio observed in the dark clouds, consistent with the possibility that they are chemically young, while translucent clouds are in chemical and dynamical steady state. For a consistent set of C/O ratios, over 80% of all model abundances investigated are within a factor of 5 of the observed abundances. Low-metal abundances and C/O ratios of 0.7 or higher are required to explain all 12 species. Distinctions between translucent and dark clouds are at most nominal. The success of the New Standard Model in explaining hydrocarbons exceeds its success in explaining all other species studied to date. In particular, hydrocarbons are better explained than the equally complex nonhydrocarbon species studied in the twelfth paper in this series.Subject headings: