When you visit Denmark, you'll probably notice that Danes glare at you, and at each other.
I have to confess that I'd made it all the way to age 50 without noticing. And I didn't start paying attention till both Sarah and Tori questioned it and went "What's the deal with the &%#)(* glaring?"
Cultural differences are both marvelous and mystifying things... and often can be found at the heart of both local and international conflict. The issue? We frame something "foreign" in the context of our "local" body of experience... and then "react" based on incorrect conclusions about the deeper meaning of what we observe and experience.
To the degree that Danes even look directly at a stranger, they will tend to come across as glaring/staring... because the "look" they give you is completely lacking in emotion. In context, they are truly "just looking" at you, not trying to "make a connection." They are not being "unfriendly." Smiles exchanged between strangers is... well... rare... because you are, after all, "strangers" and there is no (perceived) need for familiarity. In the very broadest cultural sense (and there are lots of exceptions, of course), "friendliness" is reserved for "friends."
I am reminded of someone (American) I know who visited Russia a while back, and almost felt hostility for smiling at people on the street. This did not make sense until an explanation was offered that in Russia, smiling at random strangers might even be considered rude, because "it assumes a familiarity with the other person that has not been established." To use a metaphor that might make more sense... it would be a bit like going around pinching random strangers' butt and thinking it were OK.
Historically, Denmark has been a very "formal" country. Until fairly recently, cultural behavior has been heavily governed by a type of "conforming properness;" there's a proper way to say hello, a proper time to call people, a proper time to mow your lawn, a proper time after which you start conversing quietly when sitting outside, etc. Although this is rapidly changing with the younger "Internet generations," ghosts of many of the old formalities linger.
My earliest exposure to the cultural differences between the US and Denmark came when I was just six years old. My late Godfather-- an insurance executive from New York city-- came to Denmark with his family and stayed with us for a week. He was a little distressed by me, and spent quite a lot of time and effort trying to teach me to be more "forceful" when meeting people... "shake their hand, stand tall, look 'em in the eye, and tell 'em what you know!"
At six, I thought he was a terribly rude man.
I had been taught-- at some length-- that the proper way to greet a stranger was to (briefly) make aye contact, bow your head while shaking hands (almost Japanese style, a sign of respect), and respectfully avert your eyes to indicate that you were being "friendly," not "challenging."
The second time "cultural differences" hit me square between the eyes came shortly after I arrived in the US, to go to college. I quickly learned that I was being "very rude" when I didn't introduce everyone I knew, when there was a random meeting of people on the street, or in a class, or at an event.
I had been raised with the rule that you only introduce strangers if either (A) it was relevant and purposeful for them to meet ("This is Hans, he is a plumber; this is Susan, she has a leaky pipe") or (B) you were actively intending to create a friendship between two people. I had never grown up with "casual introductions;" I was used to standing around just waiting when people would casually meet, and I didn't "need to" know them... and never thought it rude that I wasn't introduced to everyone.
When I think about it, I suppose Danes can be perceived to "glare" because the old Danish cultural mores are similar to a watered down version of my friend's experience in Russia. Smiling at someone is regarded more a "signal of familiarity" than a "random gesture of friendliness." It's by no means rude to smile at strangers... but perhaps it sends a subtle "I know you" implication that confuses people. These old values are changing, however.
Cultural differences are often subtle... and not covered in guidebooks and tourist handbooks. What's more, you usually have to experience them firsthand, because the locals often aren't aware that what they are doing "feels strange" to a visitor... at least not beyond broad stereotypes. After all, they have lived with these subtle nuances all their lives.