Generator won't hold a charge - is it the voltage regulator or the generator itself?

If the generator won't hold a charge, first thing you should check is the voltage regulator - that's usually the culprit. The simplest way to do it: disconnect the negative battery terminal and check the voltmeter reading at idle - if the voltage doesn't go above 13.5V, then the problem is definitely in the regulator. The generator itself fails less often, and you usually notice it by strange noises or a burning smell. I recommend replacing the voltage regulator first, it's cheaper and easier.

I agree that the voltage regulator is a common culprit, but don't forget about the alternator brushes either - they wear out quickly too and can lose contact. I had exactly this problem on my old car - the voltage was jumping all over the place, but the regulator turned out to be fine. The easiest thing is to first measure the voltage on the battery while the engine is running (it should be 13.5-14.5 V), and then based on the results decide what needs replacing.