"Is this common in the states? In Denmark, ..."

If they don't now, they will in a few years. We had the same evolution here in Belgium & the Netherlands, late 1990's or early 2000's recruiters wouldn't ask overly let alone require it. Nowadays they try hard to get you to disclose. I think one of the reasons is what is cited above, for the statistics for internal use. In time they will get more sophisticated and they'll start asking.

Aside, isn't there a website in Denmark where you can look up people's salaries? Or is that in Sweden?