Several times, I have read criticism of the United States which claims
that Americans are "bad" because their ancestors almost wiped out the
Native American Indian population, and because their ancestors were
heavily involved in slavery.

Setting aside the question of whether or not it is proper to blame
individuals for acts committed by their ancestors, and setting aside
the fact that most people in the world have ancestors who did these
same types of things, yet aren't blamed for them, I would like to
know:

What is the approximate current percentage of the US population that
is descended from ancestors who were NOT Americans prior to 1865, when
slavery in the US was abolished by the end of the US civil war?  In
other words, what percentage of the current US population is being
blamed for the actions of ancestors other than their own ancestors?

I did find this link:
http://www.npg.org/popfacts.htm
which tells me that "if there had been no immigration to the U.S.
since 1990, the population in 2000 would have been 262 million?19
million less than the 281 million counted. Thus, post-1990 immigrants
and their children accounted for 61 percent of population growth
during the last decade."
However, I would like to know data for post-year-1865 (or about then).

As a genealogist this type of question intriques me, but I wanted to
clarify that precise data to answer your question isn't as simple as
it sounds. When you trace someone's ancestry back as far as 1865, you
are usually back about four generations. Since the number of ancestors
multiplies with each generation (assuming no cousin marriages), then
the average American will have 16 great,great grandparents and 32
great,great, great grandparents living around 1865 (with the 16
gggrandparents being the ones most likely to have immigrated to the US
in the 1865-1890 range). Even most U.S. census results (the largest
indicator of immigration and ancestry statistics) will not take this
degree of ancestry into account. It's not too difficult to determine
the ancestry of children of post-1900 immigrants because we're usually
only talking about 2-3 generations, but when you get back 4-5
generations the likelihood increases dramatically that at least one
ancestor out of the 16 who could have theoretically immigrated to the
US around 1870 descended from someone living in the U.S. prior to
1865.

My husband's great, great grandparents, for example, immigrated to the
US in 1867 from England. Yet his grandfather married a lady who was
descended from Germans who immigrated to America in the early 1800s.
So though most of his family consists of recent immigrants, he has one
line of descent which was in America prior to 1865.

Hope this helps. If I can help find other ancestry statistics, please let me know.

--inquisitivega