Based on systematic calculations using a combined relativistic configuration interaction and a many-body perturbation theory (MBPT) approach, we provide a complete and consistent data set for 46 levels belonging to the 2s^2^2p^2^, 2s2p^3^, 2p^4^, 2s^2^2p3s, 2s^2^2p3p, and 2s^2^2p3d configurations in C-like ions with 13<=Z<=36. The data set includes energy levels as well as electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transition properties. Extensive comparisons with available observed and calculated results are made and indicate that the present MBPT calculations are highly accurate. The present data set can be used reliably for many purposes, such as the line identification of observed spectra, and modeling and diagnostics of astrophysical and fusion plasmas.