Is viscosity a function of density only? I know viscosity is also a function of temperature, but (excluding superfluids) are there any fluids which are less viscous than fluids at lower densities? Is density the ultimate control on viscosity?
 A: For the most part, temperature is the dominant factor in viscosity, not density. Unless you are also considering multi-component fluids, in which case the components of the fluid are the biggest factor.
At any rate, the typical rule of thumb is that for liquids, the viscosity decreases as temperature increases. For gases, the viscosity increases as temperature increases. This is true for both dynamic and kinematic viscosity. 
Most models for viscosity don't even factor in density. One of the simpler models, Sutherland's Law is based solely on the temperature. Obviously density and temperature are related through the equation of state, but temperature is considered the primary driver.
If we drill down to the very smallest scales, the viscosity is based on the mean free path. This is because viscosity arises through differences in translational energy of the molecules in the fluid. The collisions between the molecules serve to bring the translational energy into equilibrium, and this transfer of energy is what we call viscous forces. 
Finally, to answer your specific question: the density of ethanol is $789 kg/m^3$ and it's viscosity is $0.001095 Ns/m^2$. The density of water is $1000 kg/m^3$ and its viscosity is $0.00089 Ns/m^2$. So water is more dense, but less viscous than ethanol at the same temperature.
A: Density and temperature are important, but the forces between molecules will in my opinion be even more important.
Long chain molecules make very viscous liquids - like in the bitumen drop experiments where a drop falls every several years... looking up the density of bitumen it is very similar to that of water, but the viscosity is hugely different. 
Liquid mercury has a very high density, but is significantly less viscous than bitumen, and many lubricating oils that will have lower densities.
