Can electricity flow through vacuum?
The conductivity of the vacuum is not a very trivial issue. In fact, depending on how you look at it, it behaves in two different ways.
Firstly, there is no retarding force on any charged particle with constant velocity in vacuum. To this extent, no extra work is required in maintaining a constant current through any surface in vacuum.
In stark contrast however, is the presence of free charges in conductors. Normally, when an electric field $\mathbf{E}$ is applied across a conductor, we get a current density due to the 'internal' charge flow, given by: $$\mathbf{J} = \sigma\mathbf{E}$$ where $\sigma$ is the conductivity. Clearly, $\sigma = 0$ in a vacuum - electric fields do not spontaneously cause currents to flow. Thus, in this sense, the vacuum is not a conductor at all. Even everyday insulators have low but non-zero values of $\sigma$.
Thus, the resistance of the vacuum is in fact, infinite, as long as we define resistance in terms of the response of the charge carriers of a material. In this sense, we might say that it is an insulator - there are no charge carriers.
No, in the very basic sense it is not a good conductor, because very high voltages are required to shoot them through. But yes it still is a conductor, because it allows the flow of current.
Compare this to a diode, which similarly only allows current (in the same very basic sense) to flow if a certain voltage is applied.
Such non linear behaviour exceeds anything one would describe as basic, but if the basic sense of a conductor is that it allows current to flow, then it is a conductor indeed.
Electricity is a flow of electrons. Electrons can flow across a vacuum. The problem with doing this over a long range is that you need a force to get the electrons to travel across the vacuum.
In a CRT the cathode is heated, which gives the electrons the energy they need to escape the cathode. A large electric field then accelerates the free electrons across the vacuum and onto a target (screen). In this case, other fields are also used to steer the beam to get an optimal picture.
If you have a different system - imagine an anode and a cathode in a vacuum seperated by a small distance - with no deliberate heating taking place - then the potential difference (ie potential energy or voltage) between the two electrodes must be large eneough that the electrons can "leap" between them. They need to leap because the vacuum is a perfect insulator and so there is no medium in which they can flow (like through a metal conductor) so they must aquire all of the energy necessary to cover the distance before they can escape the cathode. Larger gap to be traversed implies larger potential difference required to get the electrons to make the leap.
Hope that helps.