The Census Bureau's website is full of valuable data. One particularly good repository is their selection of Census 2000 Briefs and Special Reports. Brief #35 analyzes ancestry data, which is more specific than race or Hispanic origin. This is really fascinating... here's the big map, which you can see in more detail in the big .pdf:What this map shows is the largest single ancestry within each county. That is, a plurality, not a majority. The big swath of light blue over much of the northern half of the country represents German. The light red along the Mexican border is, of course, Mexican. The wide band of dark purple across the farmland of the South --- and in many urban counties of the Midwest --- is African-American. The pale yellow dominating the Appalachian highlands and some other areas is, interestingly enough, simply "American."
So what does that mean? The interesting thing about the ancestry question on the Census form is that it's self-reported and open-ended, not multiple choice. So you're free to declare your ancestry however you see fit (you can report up to two ancestries, which is, curiously enough, three fewer than the number of races you can claim). So I think what "American" represents is white people whose ancestors have been in this country long enough that they've lost their identification with their ancestors' country of origin, which is probably England, Scotland, Ireland, or a combination thereof.
You may note that English and Irish ancestry seems underreported, considering this country's history. First, let's look at English, represented by the light purple you can see in northern New England and Utah. A friend of mine at work suggested that people with multiple European ancestries, like myself, are apt to report the more "interesting" of their ancestries, and English loses out because it's the default. People want to identify with the ancestry that makes them more interesting. Personally, I tend to identify with my Italian side, even though I'm actually more Irish than Italian (I believe I reported those two on my own Census form, though that leaves out my German, Swiss, English, and Spanish heritage[and Canadian, if that counts]).
I think the predominance of English in Utah may support this idea. Maybe people in Utah are just more likely to be of English ancestry, but I think what also may be at work here is that Mormons are really big into genealogy, and so it's possible that they're just more knowledgeable and accurate when reporting their ancestry. Just an idea; I don't know how I would test this theory.
Irish ancestry may suffer a bit from the same reporting bias as English, but to a lesser degree. On the map, Irish is the medium purple color that dominates Massachusetts and the Hudson River Valley of New York. Surely there are a lot more Irish in this country, right? Take a look at Table 3, Page 6 of the report. This shows the top five ancestries reported in each state. Irish ancestry is #1 in only three states, but is #2 in 19 states, plus the District of Columbia and the country as a whole. So what seems to be the case is that Irish ancestry is very dispersed. Just about everywhere you go in the U.S.A. there will be Irish people, they just don't dominate anywhere outside of the Northeast. Plus, I think, a lot of the irish ancestry is getting rolled into "American."
There are some other interesting tidbits... the light pink in northern New Mexico is for "Hispanic" or "Spanish," differentiated from the Mexican ancestry found more along the border. A lot of these people are probably those whose ancestors were here before the U.S. acquired the Southwest in 1850. Which brings us to the Native Americans, whom you can probably figure out are represented by pale orange; you can find many of the largest Indian reservations in the country by looking for that color. The white "other" category carries some interesting info, too... Cuban dominates Miami-Dade County, of course, and Chinese still has a plurality in San Francisco. The largest single ancestry in New York County (i.e., Manhattan Borough) is Dominican.