Apparently square dancing is the official state dance of numerous states, including my now-home state of Washington -- which may explain the license plates I rejected (the state park plates came, by the way, and are lovely).
My birth state of Minnesota smartly decided it didn't need a state dance...so far. I'm kinda shocked it didn't go for polka, like neighboring Wisconsin, but a little relieved, also. I guess they could also go for Minnesota Lindy, a version of the Lindy Hop.
Some interesting choices:
California--West Coast Swing
Hawaii--Hula (most natural choice on the list)
Kentucky and North Carolina--Clogging
New York--Lindy Hop
Pennsylvania--Polka, like the song
South Carolina--The Shag (apparently also known as the Carolina Shag)
Virgina--The Virginia Reel