Aperture photometry from our own observations and the literature is presented for the 12 μm galaxies in the near-infrared J, H, and K bands and, in some cases, in the L band. These data are corrected to "total" near-infrared magnitudes (with a typical uncertainty of 0.3 mag) for a direct comparison with our IRAS fluxes which apply to the entire galaxy. The corrected data are used to derive integrated total near-infrared and far-infrared luminosities. We then combine these with blue photometry and an estimate of the flux contribution from cold dust at wavelengths longward of 100 μm to derive the first bolometric luminosities for a large sample of galaxies. The presence of nonstellar radiation at 2-3 μm correlates very well with nonstellar IRAS colors. This enables us to identify a universal Seyfert nuclear continuum from near- to far-infrared wavelengths. Thus, there is a sequence of infrared colors which runs from a pure "normal galaxy" to a pure Seyfert/quasar nucleus. Seyfert 2 galaxies fall close to this same sequence, although only a few extreme narrow-line Seyfert galaxies have quasar-like colors, and these show strong evidence of harboring an obscured broad-line region. A corollary is that the host galaxies of Seyfert nuclei have normal near- to far-infrared spectra on average. Starburst galaxies lie significantly off the sequence, having a relative excess of 60 μm emission probably as a result of stochastically heated dust grains. We use these correlations to identify several combinations of infrared colors which discriminate between Seyfert 1 and 2 galaxies, LINERs, and ultraluminous starbursts. In the infrared, Seyfert 2 galaxies are much more like Seyfert Is than they are like starbursts, presumably because both kinds of Seyferts are heated by a single central source, rather than a distributed region of star formation. Moreover, combining the [25-2.2 μm] color with the [60-12 μm] color, it appears that Seyfert 1 galaxies are segregated from Seyfert 2 galaxies and starburst galaxies in a well-defined region characterized by the hottest colors, corresponding to the flattest spectral slopes. Virtually no Seyfert 2 galaxy is present in such a region. To reconcile this with the "unified scheme" for Seyfert 1 and 2 galaxies would therefore require that the higher frequency radiation from the nuclei of Seyfert 2 galaxies to be absorbed by intervening dust and reemitted at lower frequencies. We find that bolometric luminosity is most closely proportional to 12 μm luminosity. The 60 and 25 μm luminosities rise faster than linearly with bolometric luminosity, while the optical flux rises less than linearly with bolometric luminosity. This result is a confirmation of the observation that more luminous disk galaxies have relatively more dust-enshrouded stars. Increases in the dust content shifts luminosity from the optical to 25-60 μm, while leaving a "pivot point" in the mid-IR essentially unchanged. Thus, 12 μm selection is the closest available approximation to selection by a limiting bolometric flux, which is approximately 14 times vLv at 12 μm for non-Seyfert galaxies. It follows that future deep surveys in the mid-infrared, at wavelengths of 8-12 μm, will simultaneously provide complete samples to different bolometric flux levels of normal and active galaxies, which will not suffer the strong selection effects present both in the optical-UV and far-infrared.