True the Vote provides a nice report with information on voter ID laws and the politics surrounding these laws. They do a service by aggregating the number of voter suppression reports by states and county.
That’s the good news. The bad news is that their conclusions about the relationship between voter ID and turnout are wrong, or more generously, unsupported by the evidence.
The report compares turnout in states in 2008 and 2012 and attributes EVERY CHANGE to the existence (or not) of a voter ID law.
Nothing else is considered, including those things that every observer knows are the primary drivers of voter turnout: the battleground status of the state, the competitiveness of other campaigns in the state, and overall campaign spending and election activity.
Compare two of the states they highlight: Colorado, Florida, Nevada, North Carolina, and Ohio. In every state, total campaign spending was substantially higher. In every state save one (Nevada) the ratio of campaign spending was much closer, in some cases dramatically so.
Campaign spending in 2012: http://www.cnn.com/ELECTION/2012/campaign-tracker/ and in 2008: http://www.cnn.com/ELECTION/2008/map/ad.spending/
I don’t know what the impact of voter ID laws were on turnout, but I am confident that the True the Vote report doesn’t shed much light on the question.