A density functional formalism is applied to investigate the wetting behavior of Ne adsorbed on planar substrates. The study is performed over the complete range of temperatures spanned from the triple point T_t up to the critical one T_c. For this purpose, an effective attractive pair potential was built on the basis of a separation procedure. This approach yields a good description of properties of the liquid-vapor interface at coexistence in the whole range of temperatures T_t ≤ T ≤ T_c. The adsorption of Ne on alkali metals and the alkaline-earth metal Mg is analyzed. This sequence of substrates exhibit increasing attractive strength leading to a variety of wetting situations throughout the interval T_t ↔ T_c. A comparison with experimental data and other microscopic calculations is done. The predictions of a simple model are discussed. For Ne/Rb we were able to resolve prewetting lines. Results obtained from a density functional are reported for Ne/K and Ne/Mg. In the case of the latter system the interesting behavior occurs close to T_t. According to our results, Ne wets surfaces of Na and Li, and this statement is in agreement with the whole picture of the analyzed substrates.