So many subdivisions in the crime genre!
Harlan Coben, John Connolly, Lee Child, Ian Rankin, for "straightforward" crime with the emphasis on the detective
Patricia Cornwell, Kathy Reichs, and more, for forensic pathologist crime stories
Val McDermid is a British writer. and so is the hugely talented Reginald Hill, if you want an intellectual puzzle.
If you prefer the puzzle without gore, then try looking for "Cosy Crime" such as the wonderful series of Libby Sarjeant mysteries written by the UK's Lesley Cookman. Also the series of Cat Who... books, where the cats solve the mystery, by [North American] Lilian Jackson Braun.
And if you like your crime edgy, and in futuristic settings, I commend JD Robb.
If you prefer your crime mixed with comedy, then try the Janet Evanovich series. Very very funny.
For a rich variety of crime types James Patterson promotes a huge number of new crime writers' books under his name.
For a new author who writes beautifully, try Jo Cannon's "The trouble with goats and sheep", which was only published last year but has won so many awards. [Her life story is worthy of a novel in itself!]
I love all types of crime, love all of the above writers, and am rarely without a crime book in my hands.