It seems like some professors choose to retire, while others love their job so much they don't stop doing it until they die (or have health issues that make them unable to work). Which situation is more common? How common is it for tenured professors to fall into each category?
Under US law, since 1993, there is no mandatory retirement age for college faculty. They can keep working as long as they are physically able to work, and many faculty are choosing to work into their 70's and 80's. See this recent article from Inside Higher Education that gives some statistics: