Yep, but the states with sales tax get tired of getting cheated out of their tax revenue. The specific example where I saw this was a major hardware store chain in Oregon (no sales tax) right near the border of Washington (6.5% sales tax). They asked everyone “Washington or Oregon” at the register and checked ID for anyone who said Oregon.

Quick search says that Washington considers it a “sales and use” tax, so anything purchased out of state, but intended for use in Washington is supposed to be taxed. Kinda messed up, really.

In some cases like that, where you’re in a state that has no sales tax, but near the border of one that does, they’ll actually check ID and charge you sales tax if you’re from the sales tax state.