  Circumbinary accretion occurs throughout the universe, from the formation of
stars and planets to the aftermath of major galactic mergers. We present an
extensive investigation of circumbinary accretion disks, studying circular
binaries with mass ratios ($q\equiv M_2/M_1$) from 0.01 to 1 and at each mass
ratio probing the effects of disk thickness and viscosity. We study disks with
aspect ratios $H/r\in\{0.1, 0.05, 0.033\}$, and vary both the magnitude and
spatial dependance of viscosity. Although thin accretion disks have previously
been found to promote rapid inspirals of equal-mass binaries, we find that
gravitational torques become weaker at lower mass ratios and most binaries with
$0.01\leq q\leq0.04$ outspiral, which may delay the coalescence of black hole
binaries formed from minor mergers and cause high-mass exoplanets to migrate
outwards. However, in a number of cases, the disks accreting onto binaries with
mass ratios $\sim 0.07$ fail to develop eccentric modes, leading to extremely
rapid inspirals. Variability in black hole accretion correlates with disk
eccentricity, and we observe variability above the $\sim10\%$ level even for
mass ratios of $0.01$. We demonstrate that the spatial dependence of the
viscosity (e.g. $\alpha$ vs constant-$\nu$) significantly affects the degree of
preferential accretion onto the secondary, resolving discrepancies between
previous studies. Colder circumbinary disks remain eccentric even at
$q\sim0.01$ and sustain deep, asymmetric cavities.
