Now that I'm trying to do it, I find it daunting to determine what a cultivated person must know. It's quite easy to second-guess yourself, and to decide that what one learns is simply a matter of personal choice. The idea of cultivation seems elitist and arrogant; although, of course, that's not an argument against cultivation! Since so many texts are available on-line, it isn't a matter of wealth- the richest to the poorest can become cultivated in our society. But, it is a matter of time- the poor in our society are poorest in having the least amount of time to themselves.
The other question about 'cultivation' is whether or not it tends to be Eurocentric, or culturally limited in some other way. However, I can't imagine a cultivated person who has no familiarity with Confucius or Mencius. Since cultivation is essentially a matter of becoming well-rounded, it would seem to be the antithesis of any sort of 'centricity', except 'eccentricity'.
So, the first salvo in my culture crusade will be this:
The cultivated person will have read Dostoyevsky.
I was horrified in a graduate seminar a few weeks back to find that the Master's students were not only unfamiliar with Fyodor Dostoyevsky, but couldn't see the merit in reading his works. To call Dostoyevsky the greatest of all novelists is debatable. But, he is one of the greatest. And, thanks to the Internet, you can read many of his greatest works right here on Project Gutenberg. At the very least, read The Idiot, Notes from Underground, and Crime and Punishment. All are available for free on the site.