Aims.We investigate the non-Local Thermodynamic Equilibrium (non-LTE) line formation of neutral carbon in late-type stars in order to remove some of the potential systematic errors in stellar abundance analyses employing C i features. Methods: .The statistical equilibrium code MULTI was used on a grid of plane-parallel 1D MARCS atmospheric models. Results: .Within the parameter space explored, the high-excitation C i lines studied are stronger in non-LTE due to the combined effect of line source function drop and increased line opacity due to overpopulation of the lower level for the transitions considered; the relative importance of the two effects depends on the particular combination of T{eff}, log g, [Fe/H] and [C/Fe] and on the analysed C i line. As a consequence, the non-LTE abundance corrections are negative and can be substantially so, for example ˜ -0.4 dex in halo turn-off stars at [Fe/H]˜ -3. The magnitude of the non-LTE corrections is rather insensitive to whether inelastic H collisions are included or not. Conclusions: .Our results have implications on studies of nucleosynthetic processes and on Galactic chemical evolution models. When applying our calculated corrections to recent observational data, the upturn in [C/O] at low metallicity might still be present (thus apparently still necessitating contributions from massive Pop. III stars for the carbon production), but at a lower level and possibly with a rather shallow trend of ˜ -0.2 dex/dex below [O/H]˜ -1.