World Literature Today presents for your consideration the 10 greatest crime novels of all time (only 3 of them written in English), of which I've read 6.
Umberto Eco's The Name of the Rose, for which it is argued that the underlying murder mystery is a strong enough clothesline on which to hang all Eco's arcana and Borgesian techniques.
Les Liaisons dangereuses, by Choderlos de Laclos. "Most critics wouldn’t classify this great classic of French literature as a crime novel, even though the behavior within it is utterly criminal."
Also on the list: The Maltese Falcon and Crime and Punishment.
Readers are invited to nominate their contenders. I don't generally go in for crime novels, but it's obvious that the definition here is wide. I'm not convinced that Les Liaison dangereuses belongs on this list. One potential candidate I might suggest: The Daughter of Time, by Josephine Tey.
(This issue of World Literature Today also includes a short review of José Saramago's The Double, which is not strictly speaking a crime novel (although, ...), but I mention it here because I find that this novel, which I read last summer, has aged very well in my memory — were I to write about it now, I would praise it more highly.)