IIRC, aren't you supposed to calculate your owed taxes for your state and then pay when you filed? Of course not many people do this, and the IRS (or state equivalent) has no hope of enforcing this.
In some states, "use tax" is due on goods or services bought out of the state and used in the state. I don't know how widespread it is, but I don't think there's a blanket law that applies over all the US.