I've found various sites mentioning this, but non giving a complete list. The best advice seems to be to contact the national conference on state legislatures. They can usually supply information of this kind.
What States Have Franchise Tax?
I think that it's only California. All other states are considered to pay franchise taxes, but it is handled differently from California. More discretely. Kinda Makes America seem more like a corporation than a country. Hmmmmm. I guess the president of that corporation would be Obama. Now all we have to figure out is "Who is the franchise owner?" And what other corporations are being disguised as Countries.