This is one of those "it depends on the state" questions. In general, a seller is going to calculate and remit tax based on the delivery address, but the laws are actually a bit more complicated than that. chasil, who lives in Illinois but is close to Iowa, might start having packages delivered to a P.O. Box in Iowa, for example. However, legally speaking, s/he must still pay Illinois use tax on that item provided it is "for use or consumption in Illinois" and less than the current Illinois use tax rate of 6.25% was collected originally. See http://www.revenue.state.il.us/Individuals/FAQs-Use-Tax.htm

Practically speaking, of course, few people keep detailed enough records to even calculate the correct use tax owed at the end of the year, and any tax that might have been owed goes uncollected and unnoticed. Which is the problem that led to this Supreme Court case in the first place.