I always find it a bit strange and it takes me a few days to adapt, when I'm in countries where "how are you?" is a common way to greet someone (I'm from Denmark & live in Cph).

It feels very rude for me to just answer with a "great/fine/ok and you?" when someone asks me how I am, I think is has something to do with that the Danish version of that sentence (hvordan har du det?) is something that is most often said to someone when that person is having a tough time or is sick or if the person saying it is worried about the other persons emotional well-being.

Well, I'm born and raised American, and I still find it odd that people say "how are you" rhetorically here. What's the point? They even look at you funny if you respond with "Good!" Here in New York, you see an acquaintance in the halls, they say "Hey how are you," you respond "Good how are you" and the other person doesn't even answer at all! It seems extremely rude to me and I'm from here, I can only imagine what a foreign visitor thinks.

I can imagine it being odd for some foreign visitors, but plenty of other languages use similar constructs, so it should be familiar to many visitors. The American usage of how are you? or how's it going? as a friendly greeting isn't much different from the Greek τι κάνεις;, the Spanish ¿cómo estás?, the German wie geht's?, etc. In all those cases the type of answer that's expected depends on social context, ranging from a quick "fine, you?" to varying degrees of an actual answer.

As _delirium said it's probably a language/culture thing. If you were to ask an Englishman "how do you do?" the culturally acceptable thing to say, is "how do you do?" back or just to signal with e.g. a small nod that you acknowledge the greeting. And it really is just a greeting, not an actual thing someone is asking you.

(Unfortunately this carries over to all sorts of social interactions/situations that I'm not conscious/aware of, but this is one that I'm pretty sure about.)

As a dane who moved to NYC, it was really confusing. Only an hour into my stay, the subway lady asked how i was, and though i thought it was overly kind of her to ask, I told her of my exhaustion from my flight, just to be polite. she abruptly cut me off. Funny in hindsight.