Take a look at the interesting graphs at Bill Rankin's Radical Cartography; they show how population density is related to:
- racial and ethnic groups (American Indians and Alaska Natives, not surprisingly, live at the lowest population densities; what surprised me was the large amount of Hispanic population at between 1 and 10 per square mile, which Rankin says might correspond to ranchers);
- age. Roughly speaking, people ages 18 to 39 or under 5 are overrepresented at "high" densities (above 4000 or so), and other ages are overrepresented at "low" densities (below that same cutoff). This is, I suspect, a reflection of people moving to the city when they leave their parents house, and then leaving the city when it's time for their kids to go to school.
- income is highest at suburban and central-city densities, with a valley in between. Not surprising; in general the central part of a city is rich, it's surrounded by poorer neighborhoods, and then eventually income starts going up again. Rural places are poor as well.
- gender -- there are more women at high density, which I can't explain.
- population and area -- I tried to make a plot like this but had some trouble, because I was just playing around with output from another web site and didn't have the raw data.