I mostly know about book police procedurals (or legal procedurals). It's hard to just pick one country. I can pick a publisher I like - Soho Crime, not that every single author is terrific, but that I have liked most of the 50 or so of theirs I've read, and they have been set in many different countries. Many good ones set in France. http://www.sohocrime.com/
I've liked some spanish writers, whether or not from Soho press, one with a name like Riberte, but that's not it.
A lot of the procedurals set in Italy are by expats from elsewhere, so that's not quite fair, even though I've read hundreds; those tend to be written as a series though not always. Of those written by an italian, I like Gianrico Carafiglio's legal procedurals. Um, Scotland, I read most of Rankin up until just recently. Sweden, Mankell. Before I liked Mankell, I devoured the Maj Sjovall and Per Walloo books. Other Europeans, de Freeling and van Weeterling (?spelling on both) - read those early, no idea what I'd think now.
Japan, Natsuo Kirino, Miyuki Miyabe (have only read one of each) There was a male writer I read a lot of quite a few years ago, about a policeman in Osaka, forget the author's name.
Then there's Brazil.. Luiz Alfredo Garcia-Rosa, very psychology oriented police guy.
I am probably least interested now in English detective or police books/authors, having overdosed early on, reading every one of many of the authors' books.
I've have liked a lot of US authors - presently liking Joseph Kanon, he writes complicated books - usually they're not by Soho Press either, or not the ones I've ordered - since when I buy online from them, I tend to choose in part because I travel through books, always have. But, back to the US, I especially like Lorenzo Carcaterra (not everyone's cup of tea) and Richard Price; read my way through Elmore Leonard and now his son. Well, too many to mention, going back to some forties' writers. Read Hammett and Chandler early, if you think of those as procedurals. There's a present day writer I think Panzade mentioned, I'm blanking on his name.
In summary, for books that often surprise me with their stories, Soho Press. For regular favorites, maybe the US by a hair if only for sheer volume reading over decades, but on those I'm very picky. I pretty much despise best seller type stuff that's pulse written (in my view).