I don't think murder fiction is equally popular in, say, South America, but I could be wrong. It almost seems a neurosis in Denmark.
Some of my favourite Danish books are Mogens and other stories
by JP Jacobsen and The Fall of the King
by Johannes V Jensen (1944 Nobel laureate). They should be available in English, though probably in a dated translation. The Fall of The King is sort of the national novel, about the last Catholic king of Denmark who had trouble making up his mind and was overthrown. But really it's about one of the King's hengemen, Mikkel Thřgersen who wants be a great man, yet ends up a passer-by to a lot of important historical events (including the Stockholm Bloodbath, Nacka
)... and then everyone dies.
The translations are very old though, so I'm not very confident about those, though I haven't checked.
Seven Gothic Tales
by Karen Blixen are great, despite that altmodisch feel or precisely because of it. Perfect for translation I suppose, so no problem there. or maybe she actually wrote them in Danish and English simoultaneously, don't remember.
Svend Ĺge Madsen is sort of a mix between Borges and Philip K Dick, which sounds like something you've heard before, but it isn't, he's really good.
Kierkegaard I haven't truly come to enjoy, though he's probably easier to read in the English translation. There's a bit of a fuss in Denmark this year as it's the 200th year of his birth. When H.C. Andersen had the same anniversary in 2005 (I think), a lot of money wasted on tacky commemoration and everyone got really sick and tired of him. They tried to market him, didn't go too well at least not in Denmark,.. and the main event was in Parken and the head-liner ended up being Tina Turner
I often wondered what might acutally translate well, and not just 'linguistically', like you say something gets lost in translation, but also more broadly... for instance if you need to know about Danish people to appreciate the particular cynicism of The Fall of The King or whether you need to know about the city of Ĺrhus to appreciate Svend Aage Madsen.
I was surprised to learn that the magnum opus of another (internationally) forgotten Nobel laureate, Henrik Pontoppidan was translated into English recently and reviewed extensively by Fredric Jameson in the LRB. It's sort of a 'buildungsroman' (a coming of age novel) and semi-autobiographical about the son of a poor rural priest who goes to the big city (Copenhagen) to becomes an engineer and marry into an important family. He sets these impressive goals in life, but loses interrest whenever he's close to accomplishing them. Anyway, it has a very Danish ca 1900 setting and characatures a lot of Danish stereotypes (as well as actual existing figures in Danish society), and it wasn't a novel that I would've thought would make a lot of sense to non-danes. But apparantly that was a wrong idea, and now that I think about it, it does have these more international movements.. early modernism or whatever you'd like to call it + a sort of Schopenhaeuerean undercurrent (especially in the latter part of the novel). Anyway, Jameson says it better:
Once upon a time, when provinces still existed, an ambitious young provincial would now and again attempt to take the capital by storm: Midwesterners arriving in New York; Balzacian youths plotting their onslaught on the metropolis (‘ŕ nous deux, maintenant!’); eloquent Irishmen getting a reputation in London; and Scandinavians – Ibsen, Georg Brandes, Strindberg, Munch – descending on Berlin to find a culture missing in the bigoted countryside. So also Henrik Pontoppidan’s hero, an unhappy clergyman’s son who flees the windswept coasts of Jutland for a capital city which is itself narrow-minded and provincial in comparison with the bustling centres of Europe. Denmark has just lost a war, and an important territory, to Prussia: one in ‘a long row of national humiliations’ in ‘a doomed country that, in the course of one man’s life, had fallen into ruin, wasted away to a pale and flabby limb on Europe’s body swelling with power’. Denmark itself is to Europe as Jutland is to Copenhagen; and we must never underestimate the degree to which that ‘national misery’, which is secretly a part of every national history and identity, is also part and parcel of the personal or psychic identity of its inhabitants.
Both The Fall of the King
and Pontoppidan's Lykke-Per
are books everyone in Denmark has read.. or at least that was the case back when reading books was actually mandatory for you to get any kind of a diploma, which I suppose is now several decades past.