Here's a great visual to outline the percentage of American workers in a given state that are part of unions. It should come as no surprise to most people that the states with the lowest percentages are Texas, Tennessee, Virginia, South Carolina, Mississippi, Louisiana, Georgia, Arkansas, and North Carolina. The highest percentage states are Rhode Island, Michigan, Connecticut, New Jersey, California, Washington, Hawaii, Alaska, and New York.
I find it interesting that the states with the lowest percentage of workers in unions are mostly southern conservative states. These are states that traditionally go overwhelmingly republican in elections, tend to favor conservative legislation, and are the focus of GOP campaigns every reelection cycle. They are the backbone of conservative power in America, and that impact can be seen in these numbers.