We have observed 152 nearby solar-type stars with the Infrared Spectrometer (IRS) on the Spitzer Space Telescope. Including stars that met our criteria but were observed in other surveys, we get an overall success rate for finding excesses in the long wavelength IRS band (30-34 micron) of 11.8% +/- 2.4%. The success rate for excesses in the short wavelength band (8.5-12 micron) is ~1% including sources from other surveys. For stars with no excess at 8.5-12 microns, the IRS data set 3 sigma limits of around 1,000 times the level of zodiacal emission present in our solar system, while at 30-34 microns set limits of around 100 times the level of our solar system. Two stars (HD 40136 and HD 10647) show weak evidence for spectral features; the excess emission in the other systems is featureless. If the emitting material consists of large (10 micron) grains as implied by the lack of spectral features, we find that these grains are typically located at or beyond the snow line, ~1-35 AU from the host stars, with an average distance of 14 +/- 6 AU; however smaller grains could be located at significantly greater distances from the host stars. These distances correspond to dust temperatures in the range ~50-450 K. Several of the disks are well modeled by a single dust temperature, possibly indicative of a ring-like structure. However, a single dust temperature does not match the data for other disks in the sample, implying a distribution of temperatures within these disks. For most stars with excesses, we detect an excess at both IRS and MIPS wavelengths. Only three stars in this sample show a MIPS 70 micron excess with no IRS excess, implying that very cold dust is rare around solar-type stars. Comment: Accepted, ApJ; 58 pages, 7 tables, 15 figures, 16 machine-readable tables available upon publication in ApJ, or by request from the first author