The Strange Case of Dr Jekyll and Mr Hyde (1886) by Robert Louis Stevenson. Ian Rankin considers this a detective novel -- and the best one ever written -- so it belongs here. I would call it a gothic novel, and rather old-fashioned for its time, although incredibly accessible. It's a beautifully crafted and blatantly important novel. We all know the story but, I think, 99% of readers will stay engaged from beginning to end.
The Bar on the Seine (1931) by Georges Simenon. An extremely enjoyable and astute novel which begins with a conversation between Maigret and a man he has captured, who is facing the death penalty. It's the kind of book you read quickly, forget quickly, and remember bit by bit.
Rogue Male (1939) by Geoffrey Household. My goodness, some men need to get over themselves.
And Then There Was No One (2009) by Gilbert Adair. Without a doubt, objectively and unquestionably, the best postmodern detective novel of all time. But don't just read this one -- read the whole Evadne Mount trilogy.
A Study in Lavender: Queering Sherlock Holmes (2011) edited by Joseph R.G. DeMarco. This is a collection of short stories, focussing on the central Sherlock Holmes characters from a variety of LGBTQIA perspectives. The stories range in quality quite dramatically, and I think the best is Katie Raynes' 'The Kidnapping of Alice Braddon'.