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We present results from two Herschel observing programs using the Photodetector Array Camera and Spectrometer. During three separate campaigns, we obtained Herschel data for 24 stars at 70, 100, and 160 microns. We chose stars that were already known or suspected to have circumstellar dust based on excess infrared emission previously measured with IRAS or Spitzer, and used Herschel to examine long-wavelength properties of the dust. Fifteen stars were found to be uncontaminated by background sources, and possess infrared emission most likely due to a circumstellar debris disk. We analyzed the properties of these debris disks to better understand the physical mechanisms responsible for dust production and removal. Seven targets were spatially resolved in the Herschel images. Based on fits to their spectral energy distributions, nine disks appear to have two temperature components. Of these nine, in three cases, the warmer dust component is likely the result of a transient process rather than a steady state collisional cascade. The dust belts at four stars are likely stirred by an unseen planet, and merit further investigation., Comment: 11 figures, 5 tables, Accepted to ApJ