Constitutionally, states can't tax interstate commerce. That is a federal power.
A lot of states have created "use taxes" on goods purchased in another state and imported by the buyer. This is because requiring companies to withhold taxes for states in which they do not have a substantial business presence would be overly burdensome on interstate commerce. These use taxes are likely unconstitutional, but states ask their own residents to voluntarily report their cross-border sales, calculate their own tax amounts, and pay them anyway. I don't think the constitutionality has been tested from that direction, but it seems to rest upon an argument that use tax is valid, just because the goods were pulled across the border this time, rather than pushed, like all the other interstate commerce tax cases reviewed by SCotUS. As such, the only constitutionally valid use tax would be for goods purchased within your own state, for which the seller did not withhold and remit sales taxes. So cash-in-person flea market, swap meet, and classified-ad purchases, basically.
You only definitively have an obligation to pay tax on goods sold and consumed entirely within the same state. Traveling salesmen are insufficient to cause a company to qualify as having a substantial presence in a state--their sales are considered to be made in the state where their company is based, or in the state from which the actual goods were manufactured or shipped. I'd expect that e-commerce sites would be no different. If Amazon has an office, data center, or a fulfillment center in your state, you owe sales tax, and Amazon should collect it. If they do not, their site is just a traveling salesman, and your interstate purchase is subject only to federal taxes, rather than state taxes.
States bleat and squeal about loss of sales tax revenues to e-commerce sales by out-of-state companies, but they do not have a constitutional remedy for that, so too bad for them. Interstate commerce is explicitly federal jurisdiction. And Congress so far has not instituted any tariff/duty regime on goods crossing state borders. But it keeps coming up for votes, in Congress after Congress.