What makes air a good insulator? What makes air a good insulator?
My understanding of air is that its mostly just empty space with a few molecules whizzing around. Now consider a negatively charged ball suspended in air. Why don't the electrons just go into the empty space instead of staying on the ball?
 A: Your intuition behind the question is right--similar charges will try to get as far away from each other as possible regardless of whether there is air around them or not. But that is true of only free charges. 

I'm talking about random extra electrons that that have been added to the ball

Without getting into the phenomenology of the ball’s material—how do you think the charges were made to localise on the ball in the first place? Since the new charge is persistent, it was done by lowering the potential energy of the ball. This could have been done by either removing negative charges from the ball (in which case the new electrons are just a replacement for these bound ones) or by adding positive charges(in which case you have created a mechanism to bound them) or by placing the ball in some field (here the field binds them).
Of course, depending on the material, there would always be  some sort of bulk or surface potential(broken bonds, traps, lattice potential, polarization etc) and corresponding band structure responsible for binding the electrons. 
This is not to say that all electrons always stay bound to the ball…visit the ball hanging in air in a million years and you would find the charge to have changed—some charges would have escaped when the temperatures were high enough, some when the air was too humid, some others simply because they were right at the surface, some from local imperfections, some from intense light and so on. The gist is something was needed to free them.

What makes air a good insulator?

That's because below a threshold field, air on earth at STP primarily consists of electrically inert molecules in high numbers, N$_{2}$ and O$_{2}$(argon, He, water, CO$_{2}$ etc in trace). Lack of charge carriers makes it a good electrical insulator.
A: An electrical conductor is a material with electrically
charged particles (i.e. positive ions, negative ions, or free electrons)
moving around freely.
Or saying it the other way round:
An electrical insulator is a material without any electrically
charged particles moving around freely.
Now, air is a mixture of several gases:
$78$ % nitrogen ($N_2$), $21$ % oxygen ($O_2$), and some small percentages of other gases.
That means: it consists of many molecules moving around freely,
but all of them are uncharged.
Hence air is an electrical insulator.
The electrons are bound to the molecules rather tight,
meaning it would need a high energy to kick an electron
out of its molecule. Actually the ionization energy
to remove one electron from a $N_2$ or $O_2$ molecule is around $15 \text{ eV}$.
You need to compare this with the average kinetic energy
of a single molecule, which is around $0.035 \text{ eV}$
(at temperature $20 \text{ °C}$).
That's why no electrons are kicked out, when the air molecules collide.
A: 
What makes air a good insulator?

First of all I agree with the answer @lineage gave you. I would add, however, that air is a good insulator as long as the voltage between two conductors separated by air does not get high enough to ionize the air and cause it to break down. At that point, air becomes a very good conductor! So like the story about the little boy, when he is good he is very good, but when he is bad he is very bad. 
The breakdown voltage of air will depend on the separation of (gap between) the conductors and the shape (geometrical configuration) of the conductors and the air pressure, according to Pachen's Law. 
For example, the worst case for a 50/60 Hz voltage between two conductors is one where the conductors involve sharp points (making the field the most non-homogenous, that is, where the electric field strength is greatest as reflected by the density of the field lines between the conductors) and separated by an air gap of 0.01 mm at standard atmospheric pressure, the breakdown voltage is about 330 vrms.
Hope this helps by adding to @lineage answer.
A: There are three ways heat can leave your body: conduction, convection and radiation. Air is a poor conductor because it is not a solid, while silver is one of the best conductors (for electricity as well as heat) because it is a metallic solid. So, surrounded by air, your body heat won't be conducted away. Air facilitates convection, so the air surrounding your body has to be trapped in the fibres of your clothing and between the layers of clothes so that it can't convect. Air is not much good at preventing radiation (infra red), but the right kind of clothing is. So the main contribution of air to keeping you warm is that it's a very poor conductor. The reason for that is there's too much space between the molecules, so it's difficult for molecular vibrations to pass from one to the next, whereas in silver or copper, it's easy. 
