Who owns the right to reproduce your painting?

You, the artist, do. If a buyer copies it without your consent, he’s liable for damages.

The Monarch of the Glen, 1851, Sir Edwin Landseer, has been used for everything from the Hartford Insurance Company’s stag logo to biscuit tins and butter wrappers. You can read its history here
“A previous customer wants to use the painting they purchased as part of an advertising image. Anyone with experience in this?” an artist asked on Facebook. It’s a confusing subject.
The fact that her client approached her first indicates he knows that royalties are due. The artist needs to research royalties in her discipline before she can negotiate. I don’t envy her; it’s a difficult thing to pin down. 
Copyright law in the United States is different than in other countries. We have some treaty protection for our work, but nothing really protects artists from international freebooters. What I’m about to say is applicable only here. And of course I’m not a lawyer, so my advice is worth exactly what you’re paying for it.
You don’t need to register your copyright with the government for it to be protected. Copyright exists naturally once the work of art comes into existence. For something to be copyrighted, however, you actually have to make it in a tangible form. “I had that idea first!” is not a valid copyright argument, unless you can demonstrate that you actually acted on the idea.
Copyright gives you, the artist, the sole right to reproduce, create derivative works from, make prints from, and display the work publicly. It doesn’t matter if you sell the physical painting or sculpture; the rights to its image remain with you.
The Associated Press sued artist Shepard Fairey for copyright infringement for his Obama poster. The parties settled out of court in 2011, with details remaining confidential.
‘Work for hire’ is an exception to the general copyright rule. It happens when an employee creates art as part of his job or is specifically commissioned as part of a collaborative work. Advertising art done by either a salaried artist or a contracting artist is an example of the former. An example of the latter might be the artists who draw the illustrations in a medical dictionary for a commercial publisher.
An agreement that the work is for hire isn’t sufficient; the project must meet the courts’ narrow definition. Whether or not the artist is attributed makes absolutely no difference to its legal status.
String of Puppies, 1988. Jeff Koons.
Another exception is the fair-use exemption. This permits limited use of copyrighted material without the copyright holder’s permission. Fair use exemptions include research, scholarship, commentary, criticism, news reporting, parody, and search engines. Without it, artistic commentary (including mine) would grind to a halt. 
The fair use exemption doesn’t allow unlimited copying of artwork by other artists, even for self-styled ‘appropriation artists’ like Jeff Koons.
Puppies, 1985, Art Rogers. Rogers successfully sued Jeff Koons for copyright infringement, one of several times the artist has been sued.
Copyright currently lasts through the life of the author plus 70 years. If the work was produced under corporate authorship it may last 120 years after creation or 95 years after publication, whichever comes first.
What should you do if you find your painting gracing a wine label or a set of plastic dishes—or worse, badly reproduced? Consult a lawyer specializing in intellectual property. That’s theft.

Of course, anyone involved in an intellectual exchange should have a lawyer. The law is extremely complex, and expert advice is worth every penny you pay for it.

Stag for sale

“The Monarch of the Glen,” 1851, Sir Edwin Landseer

“The Monarch of the Glen,” 1851, Sir Edwin Landseer
Sir Edwin Landseer’s The Monarch of the Glen is perhaps the most widely-copied of Victorian paintings. It has been used for everything from the Hartford Insurance Company’s stag logo (c. 1867) to biscuit tins and butter wrappers.
Completed in 1851, it was part of a three-panel commission destined for the Refreshment Rooms of the House of Lords in the ‘new’ Palace of Westminster.  The House of Commons, however, balked at paying Landseer’s bill of ÂŁ150. That’s about ÂŁ17,000 in today’s money, whereas Monarch is valued at about ÂŁ10 million. Apparently, the 19th century House of Commons wasn’t very good with money.
 “Old Shepherd's Chief Mourner,” 1837, Sir Edwin Landseer

“Old Shepherd’s Chief Mourner,” 1837, Sir Edwin Landseer
Monarch was sold instead to one Lord Londesborough for 350 guineas. Londesborough sold it to Lord Fitzgerald, who in turn sold it to Lord Cheylesmore. It was owned briefly by the Pears Soap Company and sold in 1916 to Thomas Dewar, who wanted it for the Dewar whisky business in Perthshire.
From there it became a corporate asset, traveling with the Dewar’s name as it was absorbed into larger and larger companies. Eventually, Dewar’s was bought by the world’s largest manufacturer of booze, Diageo. They sold the brand but kept the stag. In 1999, Diageo loaned the painting to the National Galleries of Scotland, where it has hung ever since.
“A Distinguished Member of the Humane Society,” 1838, Sir Edwin Landseer

“A Distinguished Member of the Humane Society,” 1838, Sir Edwin Landseer. Landseer had a thing for Newfies.
Having decided that the painting has no relevance to its current brands, Diageo has decided to peddle the thing at public auction in March. If the National Galleries can raise ÂŁ4 million from the public, Diageo will donate the remainder of the value of the painting. (If you are interested in contributing, you can do so here.)
When Landseer painted Monarch of the Glen, he was working within a craze for all things Scottish. Greatly influenced by Sir Walter Scott’s romantic novels, young Queen Victoria and her husband first visited Scotland in 1842. It became one of their favorite hang-outs. Whisky itself was newly respectable after the Excise Tax of 1823 legalized its distillation. Forever after, whisky and stags have been linked together in our sentimental view of Scotland.
Landseer is most famous for his lions at the base of Nelson’s Column in Trafalgar Square, but he was a prolific and popular painter of Victorian sentimentality. When he died in 1873, all Britain mourned. By the 20th century, when Monarchwas being slogged around for advertising purposes, Landseer’s animal portraits were anathema to high-brow art critics. We are more or less past that now.
“Man Proposes, God Disposes,” 1864, Sir Edwin Landseer

“Man Proposes, God Disposes,” 1864, Sir Edwin Landseer
I can’t imagine how much money has been made by The Monarch of the Glen in its 165 years. It’s sold soap, insurance, whisky and everything else. (In modern America, artists don’t automatically transfer licensing with works of art, thank goodness.)
Diageo is under no legal obligation to give Monarch to Scotland. However, it has indirectly—through the acquisition and resale of the Dewar’s marque—made a lot of money off the old stag.  Since its net income last year was in excess of ÂŁ2 billion, it wouldn’t suffer from writing off the whole ÂŁ10 million tab.
Still, I expect the Scottish people will stump up the ÂŁ4 million. Here’s hoping that The Monarch of the Glen stays in Edinburgh forever.