We studied the rate at which stars capture dark matter (DM) particles, considering different assumptions regarding the DM characteristics and, in particular, investigating how the stellar physics influences the capture rate. Two scenarios were considered: first, we assumed the maximal values for the spin-dependent and spin-independent DM particle-nucleon scattering cross sections allowed by the limits from direct detection experiments. Second, we considered that both scattering cross sections are of the same order, with the aim of studying the dependencies of the capture rate on stellar elements other than hydrogen. We found that the characteristics of the capture rate are very different in the two scenarios. Furthermore, we quantified the uncertainties on the computed capture rate (Cχ) and on the ratio between the luminosities from DM annihilations and thermonuclear reactions (Lχ/Lnuc) derived from an imprecise knowledge of the stellar structure and DM parameters. For instance, while an uncertainty of 10% on the typical DM velocity leads to similar errors on the computed Cχ and Lχ/Lnuc, the same uncertainty on the stellar mass becomes more relevant and duplicates the errors. Our results may be used to evaluate the reliability of the computed capture rate for the hypothetical use of stars other than the Sun as DM probes.PACS numbers: 95.35.+d, 97.10.-q