  We combine a large set of quasar luminosity function (QLF) measurements from
the rest-frame optical, soft and hard X-ray, and near- and mid-infrared bands
to determine the bolometric QLF in the redshift interval z=0-6. Accounting for
the observed distributions of quasar column densities and variation of spectral
energy distribution (SED) shapes, and their dependence on luminosity, makes it
possible to integrate the observations in a reliable manner and provides a
baseline in redshift and luminosity larger than that of any individual survey.
We infer the QLF break luminosity and faint-end slope out to z~4.5 and confirm
at high significance (>10sigma) previous claims of a flattening in both the
faint- and bright-end slopes with redshift. With the best-fit estimates of the
column density distribution and quasar SED, which both depend on luminosity, a
single bolometric QLF self-consistently reproduces the observed QLFs in all
bands and at all redshifts for which we compile measurements. Ignoring this
luminosity dependence does not yield a self-consistent bolometric QLF and there
is no evidence for any additional dependence on redshift. We calculate the
expected relic black hole mass function and mass density, cosmic X-ray
background, and ionization rate as a function of redshift and find they are
consistent with existing measurements. The peak in the total quasar luminosity
density is well-constrained at z=2.15+/-0.05. We provide a number of fitting
functions to the bolometric QLF and its manifestations in various bands, and a
script to return the QLF at arbitrary frequency and redshift from these fits,
as the most simple inferences from the QLF measured in a single band can be
misleading.
