A summary of mid-infrared continuum luminosities arising from dust is given for very luminous galaxies, L_IR_>10^12^L_{sun}_, with 0.005<z<3.2 containing active galactic nuclei (AGNs), including 115 obscured AGNs and 60 unobscured (type 1) AGNs. All sources have been observed with the Spitzer Infrared Spectrograph. Obscured AGNs are defined as having optical depth {tau}>0.7 in the 9.7um silicate absorption feature (i.e., half of the continuum is absorbed) and having equivalent width of the 6.2um polycyclic aromatic hydrocarbon feature <0.1um (to avoid sources with a significant starburst component). Unobscured AGNs are defined as those that show silicate in emission. Luminosity {nu}L_{nu}_(8um) for the most luminous obscured AGNs is found to scale as (1+z)^2.6^ to z=2.8. For unobscured AGNs, the scaling with redshift is similar, but luminosities {nu}L_{nu}_(8um) are approximately three times greater for the most luminous sources. Using both obscured and unobscured AGNs having total infrared fluxes from the Infrared Astronomical Satellite, empirical relations are found between {nu}L_{nu}_(8um) and L_IR_.