The longer form of the question I'm asking: which were the key group(s) that swung from one party to another compared to the previous election? They can either be the groups that swung most dramatically, or the group whose swing (regardless of size) had the greatest impact on the election. This will almost certainly be somewhat subjective, but I still think it's worth thinking about.
In 2016, one of the key groups that swung were everyone's favorite Atlas topic: non-college whites with conservative views on racial issues and moderate-to-liberal views on economic issues.
Romney had mostly across-the-board gains compared to 2008, but two groups that stand out to me are high income voters (Obama won voters making >$200k 52-46 in 2008 but lost voters making >$250k 42-55 in 2012) and whites 18-29 (Obama won these voters 54-44 in 2008 but lost them 44-51 in 2012). The former group's swing certainly plays into the idea that a major theme of the election was a sort of low-key class warfare, as expressed by Romney's famous quote of the "
47%".
Obama reached all kinds of high-water marks in 2008, but his key pick-ups for the "Obama coalition" were young and/or non-white voters, especially in urban areas.
In 2004, the prototypical Gore-Bush voter was the "soccer mom" concerned about national security issues. Bush also made impressive improvements with Hispanic voters, as the Democratic margin fell from 27 points to 11 points.
In 2000, we have to deal with the issue of Perot's former voters returning to the two major parties; as one might expect, Bush made huge gains with self-identified independents and Republicans. Regionally, the South was the biggest difference, as it went from a rough tie in the popular vote to 13-point Republican victory; in the electoral vote, it went from a rough tie to a Republican sweep as Republicans picked up FL and the interior South. Republicans also gained a lot of ground with Hispanics (the Democratic margin fell from 50 points to 27 points).
Any agreements, disagreements, or corrections? All of the data I cited comes from Wikipedia, which is cited to either CNN Exit Polls or the Roper Center.