Some of us know that today's "best" lists are tomorrow's fish and chip wrapping, but even so I will note a strangely non-contextual collection under the title of Five Best Books: International Crime Fiction, by Geoffrey O'Brien in the WSJ.com (link sent to me by Dave Lull). An alternative link is here if the previous one does not work. The five "best" novels according to the WSJ are:
From Nine to Nine by Leo Perutz, 1918
Tropic Moon by Georges Simenon, 1933
The Fire Engine That Disappeared by Maj Sjöwall and Per Wahlöö, 1969
The Oxford Murders by Guillermo Martínez, 2005
The Water's Edge by Karin Fossum, 2007
I am sure these are all very good novels and all that (Geoffrey O'Brien's article consists of a brief paragraph about each, and that's it, no context or overview), but the "best" translated fiction? No. I have read two of these novels and would not say that they stand out from the rest of their authors' output. I have not read The Oxford Murders but if it is anything like the awful film version that I once saw on a plane, forget it. I may have read Tropic Moon, but if so, I have forgotten.
As I read quite a bit of translated crime fiction (albeit mostly modern) I thought I would write a list of five books I would recommend to anyone unfamiliar with the genre.
Miss Smilla's Feeling for Snow by Peter Hoeg.
Jar City by Arnaldur Indridason.
Shadow by Karin Alvtegen.
The Shape of Water by Andrea Camilleri.
Sun Storm by Asa Larsson.
While not claiming to be the "best", these novels will provide a good but rather modern and European-centric overview of translated (a.k.a. international) crime fiction, from a range of perspectives. If you enjoy these, I suggest you read all ten of the Sjowall/Wahloo Martin Beck series (not just one of them, as they work much better if read as a whole. Geoffrey O'Brien is quite wrong to repeat the erroneous statement that this series "owed much" to Ed McBain; they were conceived and written independently). Then you can fly solo, aided by the great resource of Euro Crime (mainly, but not entirely, European crime fiction.) Of course, any other person could write a list of five different books, which would be just as good as these.
Petrona 
Maxine – Thanks for this terrific set of recommendations! I admit, I haven’t read all of them. Still, the ones I have read are certainly among some of the finer crime fiction novels I’ve read, and I agree with you that they are representative of excellent translated crime fiction. And thanks for including the Martin Beck novels :-). I would argue that they really were the beginning of the modern generation of excellent translated crime fiction.
How could anyone say that Sjowall/Wahloo’s books owed much to Ed McBain? They stand on their own and are much better than McBain’s writings. And, they deal with Sweden’s social, economic and political system and issues, hardly something McBain would care about. Have read none of O’Brien’s list, but 3 of 5 of your list. I would have a hard time coming up with my top 5, maybe my top 20–and it would be more international than O’Brien’s.
I’ve also read none of his and 3 of yours so I guess I can’t say his list is bad but yours is excellent – even though I haven’t read the Alvtegen or Camilleri that you mention I’ve read others of theirs so feel reasonably confident in that assessment. I don’t think I’ve read widely enough yet to come up with a list of my own…though it might not stop me anyway 🙂