in the USA, it is a mixed bag. Depends on how big the vendor is "sometimes".
Some vendors do an automatic tax addon for your state. Most don't.
for the most part though, we are using the "honor system" at tax time when we fill out our Income Tax reports....
there is now a question that asks how much you purchased on the internet.
well, most of us don't bother tracking that kind of thing, and have no way of going back and capturing that kind of data, so it just gets marked as 'zero'... one of these days though, PayPal is going to be forced to report to the IRS on commercial sales. and that will plug the loop hole over here for a lot of purchases.