I live in Denmark (Copenhagen), and I can go weeks without using cash these days.
What I have is a 'Dankort' (national debit card system), so the experience doesn't necessarily transfer directly to foreign cards -- but the vast majority of places that accept
it also take at least Visa and MasterCard.
You'd need cash for bus tickets if you buy from the driver, but that's the only thing that comes to mind offhand.
travel.stackexchange.com/users/16947/hmakholm left over Monica
Credit and debit cards are extremely widely accepted in Sweden and Denmark.
Almost every vendor of anything accepts them - from big stores and hotels to small restaurants to convenience stores.
I once spent an entire week in Sweden and Denmark without once buying or spending any local currency.
My last action was to buy a small bottle of water at Copenhagen airport, and the seller waved away my apologies for using a card for such a small amount, as if to say I was apologizing for nothing.
You will probably need a chip and pin card.
travel.stackexchange.com/users/264/DJClayworth
One very important thing to note about credit card use in Denmark is that it no longer is common to have your card's magnetic strip read and then sign a receipt.
All (at least almost all) terminals in stores and hotels and hand held terminals in restaurants and even taxis expect that the card has a chip and that you know your pin code.
As for public transportation you can buy tickets at train stations with a credit card, but not in buses.
Though the bus driver has some change, don't expect the driver to be able to give change back for 100 kroner notes.
If you plan on travelling by bus, get hold of some 20 kroner coins.
Bus tickets in Denmark are area and time limited, so you can't buy a return ticket.
Only when travelling longer distances can you buy return tickets for trains
(you have to travel across regional boundaries).
travel.stackexchange.com/users/42688/Bent
I spent a week in Copenhagen this year, and I didn't use any cash at all.
I bought transport tickets from vending machines, and paid everything with my Canadian credit card.
travel.stackexchange.com/users/10087/Martin Argerami
We spent 3 weeks in Denmark and barely used any cash.
It would be easily possible not to use any at all, given that most hotels, restaurants and shops accept credit cards.
Sure, there will be a few that take cash only but nothing you cannot avoid during your stay.
We pretty much only used cash for street food and some parking.
travel.stackexchange.com/users/4801/Itai
I live in Aalborg and from my personal experience: I honestly can't remember when I last used cash.
Most stores, shops, and even hot dog stands accepts most kinds of credit cards.
Most commonly accepted cards are Visa, MasterCard, and DanCard, on rare occasions you will find a shop that doesn't accept MasterCard.
(note that since I only have experience with MasterCard I can't say if same happens with the other cards)
If however, you find a place that doesn't accept the card you use, there would most likely be a bank nearby or an ATM machine that would accept your card.
travel.stackexchange.com/users/52409/Simon Jensen
I'm from Norway where cash is about to become obsolete.
Even the strawberry seller in a booth in the field accepts credit card or mobile payments where I live.
I travel frequently to Denmark and never use cash, only visa/MC.
One thing that used to be common in Scandinavia is the use of debit-cards, this was due to "social" laws and regulations that said that no one living in these countries should ever need to buy food on credit.
This has changed over the past years and credit cards and mobile payments is widely used.
However American Express and Diners are not widely accepted same way over here as over there..
travel.stackexchange.com/users/52407/Normann
From the other answers, things have apparently changed, but here is my experience: 10 years ago in Ålborg, most grocery stores would not accept my card (MasterCard), because it was not a "Dankort".
I had to withdraw cash regularly.
travel.stackexchange.com/users/24249/njzk2
I have lived for a year in Aalborg and the only places in which I had to pay with cash were buses and certain bars (bars usually only accept Danish credit cards).
I could use my Visa in all supermarkets and stores, no matter the amount.
travel.stackexchange.com/users/52406/coderMess
In the next days I'll spend a working period (few weeks) in Denmark (Aalborg).  I would like to know if credit cards are frequently used in Denmark, are them more or less accepted everywhere in Aalborg? Or instead, do I need local currency (cash) to buy in some places?
Are credit cards prevalent in Denmark?
travel.stackexchange.com
<money><payment-cards><exchange><denmark>
travel.stackexchange.com/questions/80535
travel.stackexchange.com/users/36871/rebatoma
Cards are common for purchases of all kinds, and it is rare for a foreigner to need cash apart from in some bars that only accept Danish cards, and on buses. However, it is becoming much less common to use cards with a magnetic strip and signature. Credit card use is widespread in Denmark and most people use cash very infrequently. However, a chip and PIN credit or debit card is required. In fact, bus tickets on the bus, parking and street food seem to be the only things you cannot buy using a credit card. 
The use of credit cards is extremely widespread in Denmark. They can be used almost everywhere and cash is actually used very little. A chip and Pin card is required, however. The only things you cannot pay for in Denmark with a credit card are bus tickets on the bus, street food and parking.