Using systematic sequences of correlation consistent basis sets, the accuracy of calculated bond energies D-e(CH) and equilibrium geometries (r(e), theta(e)) has been investigated for the CHn and C2Hn series (n = 1-4). Perturbation theory (MP2, MP3, MP4), coupled cluster [CCSD, CCSD(T)], and single and multireference configuration interaction (HF+1+2, CAS+1+2) methods have been investigated. Except for the vinyl radical, all of the calculated bond energies showed significant basis set dependence with average errors (standard deviations) of 5.6 (+/-3.0) kcal/mol for the cc-pVDZ set, 1.4 (+/-0.8) kcal/mol for the cc-pVTZ set, and 0.5 (+/-0.4) kcal/mol for the cc-pVQZ set with CCSD(T) wave functions. For the vinyl radical the total variation with basis set was just 0.6 kcal/mol. Strong basis set dependence was also observed for the equilibrium geometries, e.g., for r(e)(CH) the average error decreased from 0.020 Angstrom (cc-pVDZ) to 0.003 Angstrom (cc-pVTZ) to 0.002 Angstrom (cc-pVQZ). The effect of including the core electrons in the correlated calculations was also investigated for the two series. Inclusion of core correlation in the CHn series increased D-e(CH) by 0.13 (CH) to 0.61 kcal/mol (CH2) and decreased the equilibrium CH bond lengths by approximately 0.0015 Angstrom. For the C2Hn series, correlation of the core electrons increased D-e(CH) by 0.18 (C2H4) to 1.01 (C2H) kcal/mol, but decreased D-e(CH) in C2H2 by 0.25 kcal/mol. Predictions are also made for the equilibrium geometries of C2H, H2CC, and C2H3, as well as the CH bond strength of vinylidene and the acetylene-vinylidene isomerization energy.