We went to Vatican City to visit the museums. How could you not if you're spending any significant time in Rome? There are many museums, galleries, chapels, and other collections to visit. I recommend getting there early, as it gets crowded; so much so that it takes away from the experience and leaves me in no hurry to go back. I constantly felt rushed as we were herded along like cattle down crowded corridors. I like being able to take my time through areas that interest me, but the constant flow makes it difficult to see items, much less examine them from multiple perspectives. The tour groups were particularly annoying; they stop wherever, the group surrounds the item to which the guide is speaking, and thus create both a chokepoint and an obstructed view for everyone else. But I'm not bitter. Maybe it's nicer in winter?
Since there's just so much (overwhelming), I'm just dumping a bunch of highlights. Maybe someday I'll be motivated to come back and add more detailed descriptions...
Photos within the Sistine Chapel are forbidden, hence the pic from the website. We're good tourists...we generally obey the rules.