The question comes from a comment by Mark Rovetta on my earlier question about the Earth's core going cold.
We simply don't know for sure what factors are important to the generation of a magnetic field. Mars and Venus do not have planetary magnetic fields, and while Mars is small enough for it's core to be frozen we would expect the core of Venus to still be at least partially molten like the Earth's.
A theory I have heard suggested is that the Earth's magnetic field is driven by convection currents. The Earth's core is currently solidifying, and latent heat of fusion released at the solid/liquid boundary will drive convection currents. The argument about Venus is that either the core has no solid portion, or the cooling is too slow for convection currents to form. The Venusian core could have no solid portion if it's composition is different to Earth's. Wikipedia claims this could be due to different concentrations of sulphur. Even if it does have a solid portion, Venus appears to have no plate tectonics and this could mean heat transport from the core is so slow that its core is at a nearly uniform temperature, which would mean no convection currents.
I have never heard it suggested that the presence of the Moon has any effect on the Earth's magnetic field.