Highest and lowest voter turnout percentages by state in 2012 Presidential election

All but one of the top 10 states voted for Barack Obama.  Mitt Romney won North Carolina with 50.6% of the vote.

Source (both bar graphs):  United States Election Report

6 of the 10 states with the lowest turnout voted for Mitt Romney.

And here's why I looked this stuff up.

The Most Important Article You'll Read Today About The Democratic Party.  (Daily Kos, 11/21/2015)

The author claims that West Virginia, for example, ranked 50th out of all the states in voter turnout in 2012.

Which is correct, but slightly misleading.  The list includes the District of Columbia, so strictly speaking, West Virginia ranks 49th out of the 50 states.  Hawaii takes last place.

"The most important article" is Who Turned by Blue State Red by Alec MacGillis.  (The New York Times, 11/20/2015)

In eastern Kentucky and other former Democratic bastions that have swung Republican in the past several decades, the people who most rely on the safety-net programs secured by Democrats are, by and large, not voting against their own interests by electing Republicans. Rather, they are not voting, period. They have, as voting data, surveys and my own reporting suggest, become profoundly disconnected from the political process.

 Kentucky, by the way, ranks 11th on the list of state's with the lowest percentage of voter turnout in 2012.