New far-infrared and submillimeter photometry from the Herschel Space Observatory is presented for 61 nearby galaxies from the Key Insights on Nearby Galaxies: A Far-Infrared Survey with Herschel (KINGFISH) sample. The spatially integrated fluxes are largely consistent with expectations based on Spitzer far-infrared photometry and extrapolations to longer wavelengths using popular dust emission models. Dwarf irregular galaxies are notable exceptions, as already noted by other authors, as their 500 mu m emission shows evidence for a submillimeter excess. In addition, the fraction of dust heating attributed to intense radiation fields associated with photodissociation regions is found to be (21 + or - 4)% larger when Herschel data are included in the analysis. Dust masses obtained from the dust emission models of Draine & Li are found to be on average nearly a factor of two higher than those based on single-temperature modified blackbodies, as single blackbody curves do not capture the full range of dust temperatures inherent to any galaxy. The discrepancy is largest for galaxies exhibiting the coolest far-infrared colors.