A plan to cut cash out of shopping could see Denmark become the first country to ditch notes and coins altogether.

The Danish government has proposed that most stores could dump their cash registers from January 2016.

Essential services, such as hospitals, pharmacies and post offices, would still have to accept cash under the plan, which is some way from becoming law.

Denmark, with its Scandinavian neighbors Norway and Sweden, is leading the global trend towards electronic money.

Business groups point to benefits such as reduced handling and transport costs, increased security and a drop in attempts to steal cash.

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A cashless society is "no longer an illusion but a vision that can be fulfilled within a reasonable time frame," said Michael Busk-Jepsen, executive director of the Danish Bankers Association.

Right now all retailers in Denmark must take cash. But that hasn't stopped huge numbers of Danes embracing digital options.

Nearly 40% of the population use Danske Bank (DNSKY)'s MobilePay, which allows money transfers between people, as well as purchases in stores or online.

Norway and Sweden tell a similar story.

Scandinavians rely on cash for less than 6% of all payments made. By contrast, around 47% of U.S. payments are still made with cash, according to the Norwegian central bank.

In Sweden, you can even use a card to buy street newspapers sold by homeless people. Card reader maker iZettle said sales of Situation Stockholm have jumped following the introduction of mobile payments.

And one of the country's most famous names, Abba's Björn Ulvaeus, has been a vocal supporter of a cashless society.

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The trend toward digital money is accelerating elsewhere in Europe.

Non-cash payments rose 6% in 2013, according to data from the European Central Bank. Cashless payments overtook those made with notes and coins in the U.K. for the first time last year.

Even the United Nations, alongside the Bill and Melinda Gates Foundation, wants societies to forego cash for more virtual transacting. It wants to cut costs and improve transparency, and is working with governments and the private sector to encourage more use of electronic payments.

Still, a cashless society isn't great news for everyone. Digital transacting carries growing fraud and security risks, while the elderly and marginalized groups have limited access to electronic payment options.

The most recent figures from the ECB show fraudulent use of bank cards is racking up billions in costs for unlucky consumers.

Total card fraud in Europe hit €1.3 billion ($1.4 billion) in 2012, a near 15% jump on the year earlier.