There are two big concerns with a state's ability to tax: the due process clause and the "dormant" commerce clause[0]. Quill Corp v. North Dakota[1] is the most recent SCOTUS case on point, and it really confused more issues than it settled.
The short, minimally accurate version goes like this: The analysis under the due process clause and the commerce clause looks very similar—they both deal with fairness and the connection ("nexus") the taxpayer has to the state. There is older precedent, Bellas Hess, that required a physical presence for nexus under both the due process and commerce clause. In the 67 years after Bellas Hess, the due process doctrine changed a lot, so courts around the country began to wonder if Bellas Hess was still relevant. North Dakota jumped the gun, and tried to overrule Bellas Hess for the Supreme Court. The Court was not pleased. So Quill holds that the nexus requirement is different under the due process and commerce clause. Due process does not require physical presence, but the Bellas Hess physical presence test is still the law under the commerce clause.
There are some state court decisions applying Quill every which way.
Why does this all matter? The due process limit is unavoidable, by the courts, the federal government, and the states.
The commerce clause, on the other hand, is a limit on states, but it is within congress's powers to redraw. For example, Congress clarified the state's power to tax income in P.L. 86-272.
I think states are losing revenue that is rightly theirs. Amazon has basically built a business model around avoiding sales tax. I like buying cheap stuffs on Amazon as much as anyone, but I also like having state-funded universities, decent roads, and the rest of the goods that sales/use taxes fund. States shouldn't have to suffer because so much of their economy is moving online. As long as states mind the ruptured, tangled mess left of Quill, and follow any rules thrown down by congress, I think states can get theirs without any constitutional problems.
[0] The dormant commerce clause is like the shadow of Article 1, Section 8. Congress has the power to regulate interstate commerce, so even where Congress has yet to regulate (such as use tax land), states are still prohibited from certain actions. See http://en.wikipedia.org/wiki/Dormant_Commerce_Clause
[1] http://bulk.resource.org/courts.gov/c/US/504/504.US.298.91-1...