I think 'The Silence of the Lambs' is also highly popular. The cat - and - mouse game between Clarice Starling and Hannibal Lecter is both thrilling and terrifying. It has elements of psychological horror along with crime investigation.
Probably 'Sherlock Holmes' series. The character of Sherlock Holmes is world - famous for his deductive reasoning skills. These stories are full of mysteries that he solves in the most brilliant ways.
One more popular one could be 'The Big Sleep' by Raymond Chandler. His writing style is very distinct, with a hard - boiled detective as the main character. The plot is filled with corruption, mystery, and double - crosses, which makes it a great read in the crime fiction genre.