We have recently carried out spectral synthesis modeling to determine T_eff, log g, v sin i, and [Fe/H] for 1040 FGK-type stars on the Keck, Lick, and Anglo-Australian Telescope planet search programs. This is the first time that a single, uniform spectroscopic analysis has been made for every star on a large Doppler planet search survey. We identify a subset of 850 stars that have Doppler observations sufficient to detect uniformly all planets with radial velocity semiamplitudes K > 30 m s^-1 and orbital periods shorter than 4 yr. From this subset of stars, we determine that fewer than 3% of stars with -0.5 < [Fe/H] < 0.0 have Doppler-detected planets. Above solar metallicity, there is a smooth and rapid rise in the fraction of stars with planets. At [Fe/H] > +0.3 dex, 25% of observed stars have detected gas giant planets. A power-law fit to these data relates the formation probability for gas giant planets to the square of the number of metal atoms. High stellar metallicity also appears to be correlated with the presence of multiple-planet systems and with the total detected planet mass. This data set was examined to better understand the origin of high metallicity in stars with planets. None of the expected fossil signatures of accretion are observed in stars with planets relative to the general sample: (1) metallicity does not appear to increase as the mass of the convective envelopes decreases, (2) subgiants with planets do not show dilution of metallicity, (3) no abundance variations for Na, Si, Ti, or Ni are found as a function of condensation temperature, and (4) no correlations between metallicity and orbital period or eccentricity could be identified. We conclude that stars with extrasolar planets do not have an accretion signature that distinguishes them from other stars; more likely, they are simply born in higher metallicity molecular clouds.