Ballot Box's Josh Goodman calls Utah the "ultimate anti-bellwether" state, thanks to its habit of voting anywhere from 16 to 41 points more Republican than the US as a whole.
My quibble is that a perfect bellwether picks up on shifts from one election to the next — meaning that it moves from one party to the other and back again, in much the same fashion that the entire nation does. The reverse would be a place that shifts from one party to another in the opposite direction from the nation as a whole. Utah doesn't really qualify because it's always an outlier on one side of the partisan divide.
My candidate is West Virginia, which is the only state to have voted for losers from different parties during the past six elections: Democrat Michael Dukakis in 1988 and Republican John McCain in 2008. In contrast to neighboring Ohio, which has backed every successful presidential nominee since 1960, West Virginia has been a deceiver. If you had planted yourself there during the past few decades and never left the state, you would have thought that the first George Bush and the only Barack Obama had no chance of becoming president.
Runner-up is Georgia, the only state to vote for different-party losers during the past eight elections: Democrat Jimmy Carter in 1980, Republicans Bob Dole in 1996 and McCain in 2008.
Cross-posted at Beyond Red & Blue.