This^^. Her writing isn’t especially noteworthy - it’s high quality pulp fiction, really - but she had a good line in playing with the readers’ expectations of the genre. There’s probably a reason The Mousetrap has been running in London’s West End for the last 50+ years.
Is there a definition of criteria? If it has to do with inventing the genre, then Doyle. If it has to do with popularity and number of books sold, then Christie. If it has to do with literary style, then Sayers. Does the writer have to be deceased?
Ngaio Marsh and Margery Allingham should be on the list as well, Allingham’s TIGER IN THE SMOKE is brilliant.
Still living and writing: Robert Barnard is pretty amazing, and very VERY well-written.
While I admit that Arthur Conan Doyle’s influence on the genre has been significant, Edgar Allen Poe is the one who is credited with creating the genre. “The Murders in the Rue Morgue”, featuring C. Auguste Dupin, was published in 1841. The Mystery Writers of America have named their top award for him.
Wiki link to C. Auguste Dupin
I would say that Sayers is the best writer of the bunch, but I have to give points to Christie for being able to include anybody and everybody among her possible murderers. There are some mystery writers (and I’m looking particularly at Ngaio Marsh here), where you can immediately exclude that nice young couple from all suspicion right away. And usually anybody involved in the investigation is right out. But not with Christie.
And while I love Archie Goodwin’s narrative voice, the Nero Wolfe mysteries themselves are not as strong. The standard template is 4-5 business men–could be lawyers, ad men, publishers, maybe a woman or two thrown in–and the murderer is one among them but nobody distinguishable from the bunch. Re-reading for example, “Before Midnight,” I never remember who exactly the murderer is until I’m right at the end again.
It’s hard to compare Doyle with any of the above, since this is the mainspring for the classic detective. You can see different variations on Holmes in Alleyn, Wimsey, Wolfe, Poirot, Morse, or any number of other detectives from the past century, but all have their roots in him.
My top three are Ed McBain, Andrew Vachss and Kinky Friedman.
God, I THOUGHT we had celebs secretly posting in the Dope, but … wow!
Yeah, one of those Parker guys. Not Dorothy, though.
Rex Stout.
If you need a young lady from the British Empire on your list of candidates, Ngaio Marsh.
Agatha Christie’s writing makes my eyes bleed (and makes the baby Jesus cry, which in turn, makes my ears bleed).
ETA: much as it disappoints me to see Dopers expressing admiration for Christie, I am at least heartened that no one has yet nominated Erle Stanley Gardner.
Does a writer need decades of writing to be considered? Their work adapted to the “silver screen”? A serious, traditional approach to the genre?
Do any of:
Trevanian,
Robert Ferrigno,
George P. Pelecanos,
Walter Mosley,
Harlan Coben,
Neil Barrett, Jr,
Joe Landsdale,
Dan Simmons,
Don Winslow,
G.M. Ford,
Carol O’Connell,
Randy Wayne White,
Sharyn McCrumb,
Richard Paul Russo,
Johnathan Kellerman,
John Sandford,
Stuart Woods,
<even>
Tim Dorsey,
Bill Fitzhugh or
Dave Barry
rate consideration?
Obviously, some (maybe most) would be eliminated by the word “greatest”, but shouldn’t some of these be in the running; filler in the poll, at least?
JB Fletcher. Duh!
There’s a BIG difference between a case-based procedural whodunit and hard-boiled detective writing. Comparing Agatha Christie with Dashiell Hammett makes no sense to me; completely different genres.
For Mystery/Whodunit - I acknowledge Poe’s start, but Conan Doyle and Christie established the rules within which most mystery writers write and their writing holds up not just reasonably, but excellently to this day.
For Detective - Hammett. Chandler is a great writer but a baroque stylist; Hammett at his best was Hemingway with a fedora.
My $.02
Who were both (along with Victor Appleton) Edward Stratemeyer.
What, no love for Donald J. Sobol?
Fourth vote for P.D. James, who has been my favorite writer ever since a 12-year-old me picked up a copy of Shroud for a Nightingale at a train station newsstand in 1984, while waiting to head off to summer camp. I have since read (and still own) nearly every book she has written. I have an appreciation of the greats like Agatha Christie and Sir Arthur Conan Doyle, but for my money James has the best characters, writing style, and plots.
I love me some Ruth Rendell.
Rex Stout
Gregory McDonald(more for the Flynn series than the Fletch)
Ngaio Marsh
Ellery Queen
Leslie Charteris
Can’t believe I’m the first to mention John D MacDonald.
I haven’t read many of the names mentioned here… I have read some Conan Doyle, James, Chandler, Leonard, Francis. And all of Robert B. Parker, who’s my guilty pleasure.
But greatest of all of them? I still think I’d say MacDonald.
Rex Stout.
Ruth Rendell, aka Barbara Vine. No contest.
I was sorely tempted to add his name and pretend to be serious, but I couldn’t keep a straight face at the thought of it. 
Further nomination: Enid Blyton, for the Secret Seven mysteries!
Some others that haven’t been mentioned as of post #38 -
Reginald Hill
Robert Goddard
Ian Rankin
Martha Grimes
Rennie Airth
I’m happy to have anyone nominated in the first poll - the only difference it will make is in the length of time between the first post and the poll’s appearance.