We present stellar parameters and metallicities, obtained from a detailed spectroscopic analysis, for a large sample of 98 stars known to be orbited by planetary mass companions (almost all known targets), as well as for a volume-limited sample of 41 stars not known to host any planet. For most of the stars the stellar parameters are revised versions of the ones presented in our previous work. However, we also present parameters for 18 stars with planets not previously published, and a compilation of stellar parameters for the remaining 4 planet-hosts for which we could not obtain a spectrum. A comparison of our stellar parameters with values of Teff, log g, and [Fe/H] available in the literature shows a remarkable agreement. In particular, our spectroscopic log g values are now very close to trigonometric log g estimates based on Hipparcos parallaxes. The derived [Fe/H] values are then used to confirm the previously known result that planets are more prevalent around metal-rich stars. Furthermore, we confirm that the frequency of planets is a strongly rising function of the stellar metallicity, at least for stars with [Fe/H] > 0. While only about 3% of the solar metallicity stars in the CORALIE planet search sample were found to be orbited by a planet, this number increases to more than 25% for stars with [Fe/H] above +0.3. Curiously, our results also suggest that these percentages might remain relatively constant for values of [Fe/H] lower than about solar, increasing then linearly with the mass fraction of heavy elements. These results are discussed in the context of the theories of planetary formation. Based on observations collected at the La Silla Observatory, ESO (Chile), with the CORALIE spectrograph at the 1.2-m Euler Swiss telescope and the FEROS spectrograph at the 1.52-m and 2.2-m ESO telescopes, with the VLT/UT2 Kueyen telescope (Paranal Observatory, ESO, Chile) using the UVES spectrograph (Observing run 67.C-0206, in service mode), with the TNG and William Herschel Telescopes, both operated at the island of La Palma, and with the ELODIE spectrograph at the 1.93-m telescope at the Observatoire de Haute Provence.