What is it like to live in Copenhagen without speaking Danish?

Well, I've lived in Denmark for almost 10 months now and still don't speak Danish (I know, shame on me). I have to say that you can get by extremely well on a day-to-day basis by just speaking English. Shops, banks, dentists, kebab places... no problem at all. The only situation in which I feel a little bit unsecure is when I'm in a larger group of Danish friends, where, obviously, most of them speak Danish to each other. Then I'm usually left trying to catch a few words here and there or get someone to interact with me in English. I get by for now, but it's slightly socially awkward. But, in general, you will have no problems as a foreigner speaking English in Denmark. Great place to live, btw. Btw. meme taken from this awesome Tumblr: http://whenyouliveindenmark.tumblr.com/

You can get by just fine in most of Denmark with only a knowledge of English. Denmark has a 99% English literacy rate and it's a popular language for television. Most Danes that don't speak English very well will either be immigrants to Denmark, or older people that are long out of school and have little need to keep up practice with the language. In fact, Danish is becoming lousy with English. In any event, you will be able to get by in face-to-face contact with Danes, but your lack of Danish knowledge will hamper your ability to read signage, understand announcements (such as, "this bus is going out of service"), etc. Also, despite speaking English exceptionally well, Danes will speak their native language and you can get left out of the conversation. However, if you learn even a little bit of Danish, the Danes will be suitably impressed and may even compliment you by telling you that you speak Danish better than the prince!

I spend six months studying in Copenhagen a couple of years ago (speaking no Danish) and had no issues at all (our course was conducted in English, as were all courses at the university I was attending).  People were incredibly helpful and spoke exceptionally good English across the board, I had no trouble with sorting out bank accounts, ID card or train tickets etc. Being there as a full time student I obviously wasn't in the job market but assume it would be similar to my current situation (I now live in Hong Kong and don't speak Cantonese) - it's a lot easier if you've got skills/experience in a high-demand job area and/or are looking for work with a large multinational or going for a regional (rather than national) focus. I do remember there being free language lessons available via a government agency which I considered doing but my classmates talked me out of it in favour of more UX design work.

In the EF English Proficiency Index, Denmark ranks first. This is the result of the population generally having a high level of English literacy. Statistics aside, I have never met anyone in Denmark with whom I could not have a conversation in English. As Jakob mentions in his answer, you will feel left out when Danes speak among themselves. However, they will do their best not to do so and, in my experience, they will go to great lengths to keep you in the loop. This leads to surreal situations where you're the only non-Dane at a table and people who could safely keep on their conversation in Danish do the "switch". Not to underplay the difficulty of *speaking* Danish, understanding it is much easier and will come with time. If you take a few classes, watch a moderate amount of tv and a few series or films, you'll pick up enough to understand the gist of what is being said. I say this having lived here for six months. Going back to your question, none of the day-to-day activities will be off-limits to you if you only speak English. Opening a bank account, etc. will all be possible. My bank and employer (Nordea) even sends me most documents and forms in English. The banking apps are in English as well as Danish. Danes really go the extra mile in this sense. The public administration will have fewer publications in English, but you'll always be able to talk to someone in that language. Finally, about the job: I really cannot speak for everyone. I came to Denmark with a gig waiting for me, and it was understood and implied that speaking Danish would not be a prerequisite. I also have English-speaking friends that came and found a job, but it wasn't a cakewalk and they have plenty of credentials from fancy institutions abroad. My recommendation is to look into the job market whilst you are still in your country so you can understand if Denmark can work out for you.

Everything is very easy. Not sure about getting a job, as I got a job as a researcher, which is very different in how you get jobs (you're basically expected to be a foreigner). The Danes are very good at English, and as soon as they hear you speak Danish with an accent they already switch (which is annoying if you want to practice your Danish, but of course very nice and considerate of them). Even in the bar, if I asked in Danish 'can I have a beer'. He would hear I wasn't Danish, and instead of saying something in Danish back, he'd say 'sure'.

As everybody stressed out, you can live quite well in Denmark by only speaking English. Actually, you might have a problem when you start speaking Danish: it is a hard task to pronounce the words! Seriously, there' such a thing called "tongue gymnastics" and there's nothing to do with kissing! Besides, Danes will revert to English one they realize you are struggling...I had no problems going to banks, markets, doctors. Almost everybody speaks English in upper advanced level, the exception being children and older people.My friends are nice enough to speak English to me although, of course, there will be a moment or two when they will all carry out a lively conversation in their own idiom and I will look at them feeling sorry for myself for not being able to follow up.The only problem for me is that people don't smile much and they have this extremely respect for other people's privacy which might seem like they don't care or they don't wanna know about you.Don't take it personal. It's not you; it's them.

Your main concern should be to avoid the common pitfall of staying around for 3-10+ years without ever getting around to learning Danish. Apparently one of the main challenges in doing so, is that many people habitually switch to English if anyone is still not fully confident in their Danish.That said, you'll obviously want to speak Danish if working with children or elderly, as well as for most direct service jobs. People may be bad at switching to English for conversations not particularly directed at you though (e.g. general work/social talk), so I strongly advise picking up Danish in the longer term for social reasons.

It is extremely easy... as long as you're note looking for a job. Except in expert fields, they will not hire you without danish skills, even if the job does not seem to require it.

You'll do fine with English, as pretty much everyone (at least in Copenhagen and the larger cities) speaks English fluently. Hell, I know people who don't even speak English that well and they've done fine.