There are at least five main federal limitations on state taxation, in addition to those imposed under state constitutions. Subject to these limitations, the power of states to impose taxes is plenary (i.e. unlimited).
Jurisdiction To Tax Activity Within And Outside A State
Evidently the states can tax (a) income and property of citizens and
entities within their borders; (b) commerce (via sales and excise
taxes) conducted within their borders. Has any restraint been imposed
on such taxation, other than the prohibition on double-taxation
affirmed in Comptroller of the Treasury of Maryland v. Wynne (SCOTUS,
2015)?
To impose a tax, a state must have constitutional taxing jurisdiction over the transaction or activity taxed. This question mentions a couple of examples, but there is another big basis for taxing jurisdiction that is omitted.
States can tax mail order/Internet purchases delivered to their state under a recent U.S. Supreme Court ruling, South Dakota v. Wayfair, Inc., 585 U.S. ___ (2018), overturning prior prohibitions on that practice articulated in its 1992 ruling in Quill Corp. v. North Dakota. A complex set of state laws followed, and so far, these state laws have not been harmonized with a federal statute or interstate compact.
Duties On Goods Transiting A State's Territory
One prohibition I suspect exists, but I can't find in law: Can states
impose duties on goods that merely transit their territory?
Yes. They can impose duties on goods that merely transit their territory, although, to be more exact, this is limited to inspection fees and to road use taxes based upon weight and not value.
The main U.S. Constitutional restrictions on state taxation powers are in clauses 2-3 of Section 10 of Article I which says:
Clause 2 – Taxes on imports and exports restricted
No state shall, without the consent of the Congress, lay any imposts
or duties on imports or exports, except what may be absolutely
necessary for executing its inspection laws; and the net produce of
all duties and imposts, laid by any state on imports or exports, shall
be for the use of the treasury of the United States; and all such laws
shall be subject to the revision and control of the Congress.
Clause 3 – Other conditional restrictions
No state shall, without the consent of Congress, lay any duty of
tonnage; keep troops or ships of war in time of peace; enter into any
agreement or compact with another state, or with a foreign power; or
engage in war, unless actually invaded or in such imminent danger as
will not admit of delay.
It is, in fact, routine, for this to be done in the case of semis engaged in long haul trucking which is why you see "weigh stations" along every major highway, because states can tax the use of their roads which is a form of commerce conducted in their states. Historically, this was done on a state by state individualized basis, but now there is an interstate compact, known as the IFTA, to which the lower 48 states and most provinces of Canada are a part, to which Congress has consented, governing how this is done. In practice, all of Canada, and every state except Hawaii, which for mysterious reasons doesn't have a lot of highway traffic from other states, participates.
Dormant Commerce Clause Restrictions
But, this power is limited by a doctrine known as the "dormant commerce clause" (a.k.a. the "negative commerce clause") that constitutionally invalidates state regulations that impose an undue burden on interstate commerce under an analysis similar to that used to determine if a state law is pre-empted by a federal law under the Supremacy Clause of the U.S. Constitution at Article IV, Section 1, Clause 2 which states that:
Clause 2 – Supreme law of the land
This Constitution, and the laws of the United States which shall be
made in pursuance thereof, and all treaties made, or which shall be
made, under the authority of the United States, shall be the supreme
law of the land; and the judges in every state shall be bound thereby,
anything in the constitution or laws of any state to the contrary
notwithstanding.
One of the leading dormant commerce clause cases is cited by @A.fm. in another answer to this question:
Southern Pacific Company v. Arizona, 325 U.S. 761 (1945), was a United
States Supreme Court case in which the Court held that the Arizona
Train Limit Law of 1912, which prohibited passenger trains with more
than fourteen cars and prohibited freight trains with more than
seventy cars, placed an unconstitutional burden on interstate
commerce.1 The Court held that the law imposed a burden far greater
than necessary to achieve Arizona's legitimate interest in lowering
the rate of train accidents. This case is part of the Court's
so-called negative commerce clause jurisprudence.
Prohibitions On State Citizenship Discrimination
Also relevant is Article I, Section 2, Clause 1 which states:
Clause 1 – Privileges of citizenship
The citizens of each state shall be entitled to all privileges and
immunities of citizens in the several states.
This bars inferior treatment of persons from out of state (although it is not absolute). For example, a state cannot impose different sales tax rates on stores owned by people from another U.S. state relative to locally owned stores.
Prohibitions On Federal Entity Discrimination
McCulloch v. Maryland (1819) established, on federalism grounds, that federally chartered entities and the federal government cannot be discriminated against in state taxation.
In general, the federal government and its property cannot be taxed at all by states, but, for example, the income of federal employees and income from federal bond interest and federal contracts, can be taxed on a non-discriminatory basis.
In some circumstances where a local government is heavily impacted, the federal government voluntarily pays local governments an amount in lieu of local property taxes that it would otherwise owe.
Taxes Impairing Constitutional Rights
Also, a state may not impose a tax that infringes on a constitutional right. The leading cases barred a tax that was limited to newspapers as a burden on the First Amendment free press right. Some the of case law is as follows:
The leading case in this area of law is Grosjean v. American Press Co.
(1936). A unanimous U.S. Supreme Court struck down a 2 percent license
tax that the state of Louisiana— then largely dominated politically by
its former governor and then U.S. senator, Huey Long—had imposed on
the gross receipts of newspapers with circulations of more than 20,000
copies a week. The Court recognized that it was no coincidence that
the tax fell largely on those newspapers critical of Long and his
political allies. In writing the Court’s decision, Justice George
Sutherland observed that newspapers were not “immune from any of the
ordinary forms of taxation for support of the government” but also
pointed out the dangers of differential taxation.
The Court reiterated this position in Minneapolis Star and Tribune Co.
v. Minnesota Commissioner of Revenue (1983) when it struck down a
Minnesota “use tax” on the cost of paper and products used by
periodicals in excess of $100,000 a year. Because there were only
eleven publishers—including the Minneapolis Star Tribune—that fit this
description, Justice Sandra Day O’Connor feared that the tax was
“facially discriminatory.”
Justice Thurgood Marshall came to a similar conclusion in writing the
Court’s decision in Arkansas Writers’ Project, Inc. v. Ragland (1987).
In this case, the Court overturned an Arkansas law that exempted some
specialty publications from the state’s sale tax but not general
interest magazines like the Arkansas Times. Marshall observed that “a
power to tax differentially,as opposed to a power to tax generally,
gives a government a powerful weapon against the taxpayer selected.”
By contrast, Justice Antonin Scalia, joined by Chief Justice William
H. Rehnquist, expressed the minority view that the state plan was
little different from other subsidies that the Court had upheld.
This analysis would also apply, for example, to taxes infringing on the constitutional right to access to an abortion or contraception.