(This is about the Dem primaries.)
1. Obama vote vs. black population. States with very few, and very many, black people go for Obama; states with black populations in the 8-15% range go for Clinton. This is a combination of two monotonic curves -- the white vote for Obama varies inversely with black population, whereas the black vote goes en bloc to Obama. This is generally attributed to the notion of "racial threat" -- i.e. "the more black people you see the less likely you are to vote for one."
2. Obama vote vs. Republican population in heavily white areas. Counties with very few, or very many, Democrats are relatively strong for Obama; "swing" counties for Clinton. Heavily Dem counties favor Obama largely because they tend to be urban, young, and relatively heavy-minority. The other end of the parabola is slightly more puzzling, but very persistent. Jay Cost shows that this effect held even in Central Pennsylvania, where everything else was going against Obama. (He lost several counties by 20% that he was supposed to lose by 30-35%.) So, Cost now suggests, Obama did better in Indiana than Ohio -- which has similar demographics -- because it's so Republican. He explains this by saying that culturally conservative Dems prefer Hillary, but in heavily Republican areas the cultural conservatives tend to be Republican.
I think these are both causation-correlation fallacies to some extent, though it's hard to control for all the variables. Some observations:
A. Hillary's strength among whites in southern states is at least partly an artefact of her overwhelming strength in Appalachia, which is almost entirely white and would fall on the "Obama" part of parabola 1 (see: WV, KY). Carving off the Appalachian parts of VA and NC increases Obama's percentage of the white vote in those states. Besides, the most heterogeneous counties are all cities, and Obama seems to do OK with the urban white vote (though cities are wealthy and that helps him).
B. The other geographical feature of note is that Obama dominates the entire upper midwest and northwest. These states are all very white, and a lot of them are heavily Republican. Is Obama benefiting from the exodus of racists etc. to the Republican party? And how about Wisconsin and Iowa, which are not particularly rich and not particularly Republican? Is the determining factor something else that's correlated with geography? Why is there less "racial threat" in these states than in WV? The notion that there's something geographical about this, btw, has some support from Cost's data. He notes somewhere that NW Ohio and Indiana were a lot less pro-Hillary than SE Ohio despite similar demographics. (It's also more Republican, which fits his pattern.) Indiana was apparently even less pro-Hillary than NW Ohio. Is this just because it's further west?
C. Five-thirty-eight says the time series data shows that some aspects of the race have changed since January, e.g. it used to be that the liberals went for Hillary and the moderates for Obama; recently it's been the other way round. You could put this down to Rev. Wright etc. If this were substantially true it would invalidate parabola 1. I think the time-series is just an artefact of the order in which different states voted, i.e. Obama would've drawn the "liberals" in PA and the "moderates" in Iowa and NH no matter what. He's still polling well ahead of Hillary in Iowa, which has a lot of "moderates." On the other hand, states outside of Appalachia are probably more susceptible to "momentum"; only diehard Hillary fans would even bother to go vote for her at this point.
I feel like there probably ought to be something to both the arguments I've been quibbling with. However, they're really not that solid, and there do seem to be people out there who should have the time to clean them up and test them.
Update. Exit data from Oregon backs me up on point C. Obama won the weekly churchgoers, just as he had in Iowa and NH.