But now Sweden and Denmark are involved in a new spat – over the unlikely matter of floor coverings. And Sweden's omnipresent homeware retailer, Ikea, is at the heart of the row.
The firm has been accused of "cultural imperialism", for encouraging its customers to walk all over Denmark, by giving its mats and carpets Danish names.
In contrast, its top-end products, such as sofas and beds, are named after Swedish, Norwegian or Finnish cities.
The style slight was uncovered following what appears to have been an analysis of the firm's catalogue by Klaus Kjller, of the University of Copenhagen, and Trls Mylenberg, of the University of Southern Denmark.
Mr Kjoller said: "Doormats and runners, as well as inexpensive wall-to-wall carpeting, are third-class, if not seventh-class, items when it comes to home furnishings."
He said Ikea's naming convention portrayed Denmark as the doormat of Sweden, a country with a larger economy and population.
The researchers concluded that Swedish names were reserved for the "better" products, and that even Norwegian ones managed to make it into the bed department.
But the "lesser" products bore Danish names, such as "Roskilde" and "Kge".
Ironically, if history had taken a different course, Ikea would be Danish today. Its founder, Ingvar Kamprad, set up his business in Scania, which has been a battleground between the two countries.
Bloggers – always ones for conspiracy theories – have jumped on the analysis and claim it shows that underneath Ikea's quirky image lies a dark imperialism. Unsurprisingly, that is not a description with which Ikea identifies.
It says the issue is all innocent – and, anyway, having a floor covering named after you is actually a compliment, according to the firm.
"It's nonsense to say that we did this on purpose. It was a pure coincidence, and it happened many decades ago," said Ikea spokeswoman Charlotte Lindgren.
She noted that the employee who had come up with the product names had long since retired.
Ms Lindgren went on: "Besides, these critics appear to greatly underestimate the importance of floor coverings.
"They are fundamental elements of furnishing. We draw worldwide attention to Danish place names with our products. That has to be a positive thing."
Her explanation may not be enough to mollify the Danes. Under one plan for revenge, the Carlsberg brewery could give one of its light beers – which the Swedes hate – a Swedish name.
Historical catalogue of disputes gives clue to rivalry
THE Danes' sensitivity over apparently innocuous furniture brand names can perhaps be explained by a look back over Denmark's history with Sweden.
The countries have bickered for centuries – with the Danes the underdog more often than not. Countless wars, peace treaties and diplomatic efforts have created today's borders.
Wealthy Norway once belonged to the Danes – until the Swedes took it away and eventually granted it independence more than 100 years ago.
The southern Swedish Scania region – where Ikea is based – was once Danish.
Even the countries' capitals, Stockholm and Copenhagen – which are roughly the same size – compete against one another to be the capital of the region.
One of the first sights to greet passengers arriving at Stockholm's Arlanda Airport is a giant sign meant to eliminate all doubts – "Welcome to the capital of Scandinavia".
As far as Denmark is concerned, Copenhagen is Scandinavia's most successful economic zone.
WHAT'S IN A NAME FOR SCANDINAVIAN
SKGE is one of the best preserved medieval towns in Denmark and lies in Roskilde county on the east coast of the island of Zealand in the east of the country. It is also an Ikea door mat.
Roskilde is the medieval capital of Denmark. Its music festival will this year host Neil Young and The Streets. It is also an Ikea rug.
Niv, on the island of Zealand, has a strong immigrant population, which often clashes with the locals. It is also an Ikea flooring lining.
Strib is a town in Funen county, Denmark, which contains the country's only red telephone box. It is also an Ikea rug.
Helsingr is known in English as Elsinore - the setting for Shakespeare's Hamlet. It is an Ikea rug.
Malm is the administrative centre of Verran in the county of Nord-Trndelag, Norway, and once an industrial centre. It is also an Ikea bed and bedside table combination.
Leksvik is an old farming and lumbering community in Norway, which is developing its high-technology industry. It is also an Ikea range of furniture, including bookcases.
Flarke is a small village in Vasternorrland, Sweden. It is also an Ikea bookcase.