Does charge density in a circuit match potential? In a typical circuit, there is a high potential at one end, and this decreases (across resistance) to a low potential at the other end. Does this imply that there is a positive charge (not many electrons)  in places of high potential, and a negative charge (lots of electrons) in places of low potential? If so, would that suggest that the electrons that form a current become more spaced out as they travel along the circuit?
 A: 
Does this imply that there is a positive charge (not many electrons) in places of high potential, and a negative charge (lots of electrons) in places of low potential?

Yes, but you should not that in equilibrium conditions, charges will not accumulate in the interior of a conductor of uniform resistivity and uniform cross section. Rather, the charges will accumulate on the surfaces of such conductors, or the interfaces where resistivity or cross section changes.
So, on a wire which has a voltage drop through it, there will be more electrons on the surface of the wire on the negative end, and less electrons on the surface of the wire on the positive end. If the wire is straight, the charge on the surface will change gradually from one end of the wire to the other. If the wire has a curve to it, the charge density on the surface on the inside of the curve will be different from the charge density on the surface on the outside of the curve.

If so, would that suggest that the electrons that form a current become more spaced out as they travel along the circuit?

That would be the case if it were not for the fact that electrons interact with the atoms of the conductor (and other electrons). Electrons in a conductor in which there is an electric field accelerate toward the positive potential for a short distance, and then collide and their motion becomes randomized. Then they begin accelerating again, collide again, and so on. The mean free path, (the average distance which the electrons travel between collisionis) is very small. As a result, the drift velocity, that the electrons develop is usually very small. Amazingly, the drift velocity of electric current flowing in a wire can be slower than the speed of a human walking. You may think of the analogy of a mild breeze. The atoms in the atmosphere are traveling on average somewhere near the speed of sound, hundreds of miles per hour, but the breeze may be only a few miles per hour.
