</font><font color="blue" class="small">( I had someone tell me that I didn't owe sales tax, and I wanted to be sure that I didn't break the law. )</font>
Technically, you don't owe "sales" tax to the state the item is purchased from if the item is shipped out of state (via a common carrier, USPS, etc) to a state that the seller does not operate a physical entity. However, you do owe "use" tax to your home state (the destination state the goods are shipped into) for that same purchase. "Use" tax is typically charged at exactly the same rate as "sales" tax. So the tax would be the same as paying your local sales tax rate.
LEGALLY and MORALLY you could pay the tax to the sellers state, if the sellers state has a lower sales tax rate, and that would be totally legit. For the example of N.H. and I believe Alaska??? where there is no sales tax, you could legally buy the good in that state and bring it home, but you would be doing the transportation, not a common carrier, USPS, etc. I am not up on ALL the state laws, but most states would not be able to come back and charge you the home state tax on a good that you picked up in a different state, if you paid the tax on the good in that state.