In order to investigate the formation of O I 7771-5 and [O I] 6300/6363 lines, extensive non-LTE calculations for neutral atomic oxygen were carried out for wide ranges of model atmosphere parameters, which are applicable to early-K through late-F halo/disk stars of various evolutionary stages. The formation of the triplet O I lines was found to be well described by the classical two-level-atom scattering model, and the non-LTE correction is practically determined by the parameters of the line-transition itself without any significant relevance to the details of the oxygen atomic model. This simplifies the problem in the sense that the non-LTE abundance correction is essentially determined only by the line-strength (W_{lambda}_), if the atmospheric parameters of Teff, logg, and {xi} are given, without any explicit dependence of the metallicity; thus allowing a useful analytical formula with tabulated numerical coefficients. On the other hand, our calculations lead to the robust conclusion that LTE is totally valid for the forbidden [O I] lines.