Also, check the voltage regulator. I suspect that a lot of generators are changed out when the regulator really is the problem.
The regulator has two relays; one is the cutout and the other is the regulator. (I can never remember which is which; check a shop manual.) Make sure the contacts on the regulator relay are clean. Just pulling some rough paper through it (e.g., from a brown paper bag) might be enough; if not, you can get a tool to clean relay contacts from an electronics store. It's a flat piece of metal with diamond dust in its surface. The conventional wisdom is not to use fine sandpaper; not sure why. Some people do it, though. Be sure to disconnect the battery before doing this!
There is also a procedure for checking its operation; you can find it in any shop manual. Requires an analog voltmeter. If you have one, it's worth doing, too. If not, just clean the sucker and see if that helps.
Generator brushes are a real possibility, too, of course.