Fantastic responses. Let's see if I'm understanding this correctly.
1.) Current is comparable to a line of, say, beads. The beads are situated all the way around the circuit (not moving) before voltage is applied. Then, once voltage is applied, those beads start to move. So it isn't a sequence of events (current comes out of the negative terminal, flows through the resistor, then reaches the LED), but rather a cycle of "beads" that are already situated around the entire circuit.
2.) The location of a resistor (or any other component) is irrelevant, because, in the case of a resistor, if one section of the "chain of beads" is slowed down (the current is resisted), the entire chain slows down.
Assuming the above statements are correct, I think I understand this now. I'm used to thinking of things sequentially (I'm a programmer, after all), but that doesn't appear to be the case with electronics.
Am I on the right track?