Here's a list of classic novels that are essential reads in the Crime and Suspense genres. The list is roughly chronological, ranging from the 1930s to the current time. Note that the list does not include traditional Mystery novels, which is a separate genre.
The Maltese Falcon - Dashiell Hammett. Where the terse, hardboiled style all began.
The Big Sleep - Raymond Chandler
Double Indemnity - James M. Cain. The classic Noir doomed crime plan.
The Getaway - Jim Thompson. The crime novel as a descent into Hell.
The Manchurian Candidate - Richard Condon. The paranoid conspiracy thriller and a monstrous maternal figure.
Psycho - Robert Bloch.
The Deep Blue Goodbye - John D. MacDonald
The Friends of Eddie Coyle - George V. Higgins. Gritty crime story told in pitch perfect street dialogue. Elmore Leonard learned from this author.
Death Wish - Brian Garfield. Unban crime problems and the novel of revenge.
Tinker, Tailor, Soldier, Spy - John LeCarre. The perfect Cold War spy novel.
The Ipcress File - Len Deighton. The spy novel retold with working class cynicism.
Marathon Man - William Goldman. That shudder-grating torture scene in a dental chair.
Miami Blues - Charles Willeford. An under-appreciated gem of a crime author.
Killshot - Elmore Leonard.
The Black Dahlia - James Ellroy. Frantic, pitch black, and borderline insane, as only Ellroy can write.
Silence of the Lambs - Thomas Harris. The best serial killer novel ever written.
Heaven's Prisoners - James Lee Burke
Mystic River - Dennis Lehane.
No Country For Old Men - Cormac McCarthy. Noir fatalism in the new West.
City of Bones - Michael Connelly. The police procedural at its best.
The Leopard - Jo Nesbo. Obsession, Nordic style.