You might find that the only way to gather this information is through solid research, starting somewhere like the The Royal Library.

Do you mean popular in a lot of Danish non-fiction books, or popular in popular Danish non-fiction books?

Would that be popularity as measured by number of books printed, or by the number read?

How does the number of editions factor into this?

For titles or body text?

You see, I don’t think it is possible to accurately answer such questions.
The usual method is to accept the opinion of an expert, which is little better than anecdote, IMO.

Over 12,000 books were published in Denmark in 1996 (the latest year the article had stats for), so I doubt if anyone is keeping track of overall font usage. But perhaps if you contacted some of the major publishers, you might find someone willing to give some guidance.

http://en.wikipedia.org/wiki/Books_published_per_country_per_year

In the English-speaking world, non-fiction typography, depending on what field one is looking at, has tended to be dull, at least at some levels.

Today, almost everything is in Times Roman. Yesterday, science textbooks were overwhelmingly in Modern series 7 because of the availability of mathematical symbols from Monotype in that typeface. And if you go back to the 18th Century, Caslon was used for just about everything.

Of course, if you go to non-fiction books for which a huge popular sale is anticipated, more will be invested in the typography. Times Roman is still quite likely, but you could get Baskerville, you could get Palatino... or you could even get Optima or Univers, particularly if the book is concerned with the arts rather than the sciences.

Caledonia and Century Expanded are more likely to be found as alternatives to Times Roman for works of fiction, although they're used for non-fiction as well.

But there isn't enough effort expended on a more diverse range of typefaces in huge swaths of the book publishing industry. Magazines, as vehicles for advertising, receive more attention in this regard.