Mid-infrared spectroscopic measurements from the Infrared Spectrometer (IRS) on Spitzer are given for 125 hard X-ray active galactic nuclei (AGNs; 14-195 keV) from the Swift Burst Alert Telescope (BAT) sample and for 32 AGNs with black hole masses (BHMs) from reverberation mapping. The 9.7 mu m silicate feature in emission or absorption defines an infrared AGN classification describing whether AGNs are observed through dust clouds, indicating that 55% of the BAT AGNs are observed through dust. The mid-infrared dust continuum luminosity is shown to be an excellent indicator of intrinsic AGN luminosity, scaling closely with the hard X-ray luminosity, log nu L-nu (7.8 mu m)/L(X) = -0.31 +/- 0.35, and independent of classification determined from silicate emission or absorption. Dust luminosity scales closely with BHM, log nu L-nu (7.8 mu m) = (37.2 +/- 0.5) + 0.87 log BHM for luminosity in erg s(-1) and BHM in M-circle dot. The 100 most luminous type 1 quasars as measured in nu L-nu (7.8 mu m) are found by comparing Sloan Digital Sky Survey (SDSS) optically discovered quasars with photometry at 22 mu m from the Wide-Field Infrared Survey Explorer (WISE), scaled to rest frame 7.8 mu m using an empirical template determined from IRS spectra. The most luminous SDSS/WISE quasars have the same maximum infrared luminosities for all 1.5 < z < 5, reaching total infrared luminosity L-IR = 10(14.4) L-circle dot. Comparing with dust-obscured galaxies from Spitzer and WISE surveys, we find no evidence of hyperluminous obscured quasars whose maximum infrared luminosities exceed the maximum infrared luminosities of optically discovered quasars. Bolometric luminosities L-bol estimated from rest-frame optical or ultraviolet luminosities are compared to L-IR. For the local AGN, the median log L-IR/L-bol = -0.35, consistent with a covering factor of 45% for the absorbing dust clouds. For the SDSS/WISE quasars, the median log L-IR/L-bol = 0.1, with extremes indicating that ultraviolet-derived L-bol can be seriously underestimated even for type 1 quasars.