Apparently Ohio still prohibits transportation of alcohol (even for personal use) across its state lines, without a license ("H permit"), while Pennsylvania legalized it in 2015/2016 and Iowa was considering doing the same in 2018.
Even in states where (and when) it was still illegal, these laws are apparently hard to enforce (and also unknown to many).
Is there a more complete picture in which US state transporting alcohol into the state is still illegal even for personal use, without a license?
Grovkin's answer centers on Granholm v. Heald, but this probably not sufficient to completely answer the question. E.g. a 2011 NYT article mentions that
In the six years since [Granholm v. Heald], several states have liberalized their wine laws. But many restrictions remain.
Alabama oenophiles can order wine only from an out-of-state producer if they have received written approval from the state’s Beverage Control Board. Wineries can ship into Indiana and Delaware only to consumers who have visited the winery and made a purchase in person. In 37 states, residents are prohibited from ordering wine from online retailers or auction houses or even joining wine-of-the-month clubs.
Possibly such states are prolonging their lucrative tax advantage while waiting to be sued following Granholm v. Heald, or the latter decision doesn't fully cover the need to acquire a license to transport alcohol across a state border.
The Wikipedia article that Grovking linked/quoted also mentions that
Different states have enacted different regulations. An editorial article on the commercial wine selling web site Appelation America says that many of the conditions in these regulations are either so complex or so expensive as to discourage wineries from complying.
Which seems to imply that a [state] license is still needed for on-line sales (including from out-of-state wineries). Given that, presumably states can still require a transportation [across state border] license as well, if their laws require one, despite Granholm v. Heald. Also, the Pennsylvania and Iowa press articles on liberalizing their transportation laws don't mention Granholm v. Heald at all.
And we're getting into a big aside here, but even for direct shipment, on which better information can be found on-line
The majority of states have statutory provisions that allow for out-of-state manufacturers to ship alcoholic beverages directly to consumers. The majority of states restrict the direct shipments to wine.
Out of the 54 states, territories and commonwealths, three states—Alabama, Oklahoma and Utah—specifically prohibit the direct shipment of alcoholic beverages to consumers. Mississippi, Guam, Puerto Rico and the U.S. Virgin Islands do not have statutes that specify that direct shipments are allowed. Massachusetts and Pennsylvania have had statutes ruled unconstitutional by state courts in those states.
Delaware have statutory provisions that require orders to be processed and shipped through licensed wholesalers. Arizona, Arkansas, Georgia, Kentucky and South Carolina have statutory provisions that allow wine to be shipped into the state when purchased by the customer on-site at the winery. Rhode Island allows intoxicating beverages to be shipped when purchased on-site.
Five states—Arizona, Florida, Hawaii, Nebraska and New Hampshire—and the District of Columbia authorize the direct shipment of all spirits as specified. Eight states allow the direct shipment of beer and wine as specified: Delaware, Massachusetts, Montana, North Dakota, Ohio, Oregon, Vermont and Virginia. The remaining states only allow direct wine shipments.
And note that being able to ship doesn't mean no license is required for that, e.g.
Tex. Alcoholic Beverage Code Ann. §16.09
(a) The holder of a winery permit may ship wine to the ultimate consumer, including ultimate consumers located in dry areas. Delivery must be by the holder of a carrier permit.
This doesn't answer my question about personal transportation though. Texas does have a personal transportation exemption, but is pretty convoluted, still requiring a Texas tax even without a permit:
Sec. 107.07. IMPORTATION FOR PERSONAL USE; [...]. (a) A person may import not more than 24 12-ounce bottles or an equivalent quantity of malt beverages, 3 gallons of wine, and 1 gallon of distilled spirits for the person's own personal use without being required to hold a permit. A person importing alcoholic beverages into the state under this subsection must pay the state tax on alcoholic beverages and an administrative fee of $3 and must affix the required tax stamps. [...] A person importing alcoholic beverages under this subsection must personally accompany the alcoholic beverages as the alcoholic beverages enter the state. A person may not use the exemptions set forth in this subsection more than once every thirty days.
Perhaps worth mentioning: Texas gives in Sec. 107.11. an exemption from the 107.07(a) tax & quota for the "IMPORTATION OF PERSONAL COLLECTION" of someone relocating their household into the state.
So in view of the latter, I guess a better question would be (rather than outright import ban without a license/permit): how many states require a state [alcohol] tax even on [personal] transports for personal use?