The court fights over Voter ID are interesting. The reality is that most of these laws are being blocked because they went well beyond simply requiring a voter to display id. Many of these laws altered early voting, voting locations, registration requirements, absentee voting, motor voter rules, and other rules regarding voting.
If the state legislatures had simply stuck with requiring a picture id to vote (which I support) then most of laws would have easily withstood court challenges.
However because state legislatures through-in every restriction imaginable (including some I don't support) most of these "voter id" laws became easy targets in court - it became simple for civil rights organizations to demonstrate that the rules restricted and suppressed the rights of voters.
If the Republicans driving these laws had even minimal common sense then they would have stuck with voter id laws that simply required the display of picture ids at the voting location (to prevent fraud) - and not tried to shove all sorts of other restrictive requirements into the law that obviously are designed to suppress the voting of citizens.