Characters that I have revisited
Mma Ramotswe - Botswana - Alexander McCall Smith writes about the No. 1 Ladies Detective Agency, headed by this woman
Bertie - Scotland - a 7 year old genius with a very bothersome mother, also A.M. Smith
Inspector Rostnikov - Russia - Russian police stories by Stuart Kaminsky
Lord Emsworth - England - befuddled English lord by P.G. Wodehouse
John Dortmunder - New York - head of gang of thieves by Donald Westlake
Jake Lassiter - Miami - smart, tough lawyer by Paul Levine
William French, M.W. (failed) - London - wine merchant with dog by A. M. Smith
Commissario Guido Brunetti - Venice - Venetian policeman by Donna Leon
Tenzing Norbu - Los Angeles - Tibetan monk formerly on the LAPD police, now private investigator
Prof. Don Tillman - Australia - Asperger's syndrome prof. of genetics by Graeme Simsion
Cormoran Strike - London - detective by J.K. Rowling
Elvis the Newfoundland - America - Newfoundland dog meant to protect US President by Jenny Lee
Lord Peter Wimsey - London - Nobleman who is detective by Dorothy Sayers
Darko Dawson - Ghana - Ghanaian policeman by Kwei Quartey
Jim Chee - New Mexico - Navajo reservation policeman by Tony Hillerman
Bernadette Manuelito - New Mexico - also Navajo police by Tony Hillerman
Arkady Renko - Russia - Russian policeman often in trouble with Russian police by Martin Cruz Smith
Armand Gamache - Montreal - French Canadian police by Louise Penny
Kate Fansler - New York - Columbia prof. solves crimes by Amanda Cross
Flavia de Luce - England - child genius chemist by Alan Bradley
Joe Gunther - Vermont - by Archer Mayor
Kate Chandler - New York - employs magic by Shanna Swendson
The Man in the Yellow Hat - America - Curious George, child's book by H.A. Rey
Cassie Maddox - Ireland - Tana French writes about Dublin police
Myron Bolitar - America - adventures of a sports agent by Harlan Coben
Josiah Reynolds - Kentucky woman by Abigail Keam
Hamish MacBeth - Scotland policeman by M.C. Beaton
Agatha Raisin - England detective by M.C. Beaton
Lewellyn Ferris - Wisconsin Rhinelander police by Victoria Houston
Lisbeth Salander - Sweden - weird but brainy girl by Stieg Larsson
Clare Fergusson - upstate New York Episcopal woman priest by Julia Spencer-Fleming
Brown Dog - Michigan - dissolute ne'er-do-well by Jim Harrison
Grady Service- Michigan - super game warden by Joseph Heywood
Anna Pigeon - National parks policewoman by Nevada Barr
Others have suggested