We have carried out a sensitive search for gas emission lines at IR and millimeter wavelengths for a sample of 15 young Sun-like stars selected from our dust disk survey with Spitzer. We have used mid-IR lines to trace the warm (300-100 K) gas in the inner disk and millimeter transitions of (CO)-C-12 to probe the cold (similar to 20 K) outer disk. We report no gas line detections from our sample. Line flux upper limits are first converted to warm and cold gas mass limits using simple approximations allowing a direct comparison with values from the literature. We also present results from more sophisticated models following Gorti & Hollenbach that confirm and extend our simple analysis. These models show that the [S-I]25.23 mu m line can set constraining limits on the gas surface density at the disk inner radius and traces disk regions up to a few AU. We find that none of the 15 systems have more than 0.04M(J) of gas within a few AU from the disk inner radius for disk radii from 1 to similar to 40 AU. These gas mass upper limits even in the eight systems younger than similar to 30 Myr suggest that most of the gas is dispersed early. The gas mass upper limits in the 10-40 AU region, which is mainly traced by our CO data, are < 2 M-circle plus. If these systems are analogs of the solar system, they either have already formed Uranus- and Neptune-like planets or will not form them beyond 100 Myr. Finally, the gas surface density upper limits at 1 AU are smaller than 0.01% of the minimum mass solar nebula for most of the sources. If terrestrial planets form frequently and their orbits are circularized by gas, then circularization occurs early.