Conan Doyle, of course, famously did. Sherlock Holmes "died" at the Reichenbach Falls in 1893, and returned in "The Empty House" in 1901. This week, David Pirie's BBC2 drama The Strange Case of Sherlock Holmes and Arthur Conan Doyle presented the first demise as a spin-off from the author's family traumas. In Arthur & George, Julian Barnes takes a much brisker view, with Holmes's creator embarrassed by the sleuth's snowballing global cult but unable to withstand the financial temptations to bring him back.
Conan Doyle was the first of many successful crime writers to feel tugged between the easy rewards of a serial investigator and the drive to explore fresh characters and forms. The better the author, the sharper the tension. Over the past few years, Michael Dibdin's series about his maverick Venetian detective Aurelio Zen has offered a piquant, double-edged fascination. Zen, whose superbly written early outings in novels such as Ratking and Cabal made a nonsense of the distinction between "genre" and "literary" fiction, has gone on solving his cases, annoying his bosses, and dodging the gruesome beasts that lurk in modern Italy's various underworlds. At the same time, Dibdin has sometimes seemed as frustrated with his hero as Zen is with his job, and just as keen to play games and break rules.
In Back to Bologna (Faber, £10), Dibdin junks the traditional whodunit in favour of a sort of literary operetta. This gaudy squib abounds with in-jokes, caricatures and sitcom-style stunts. The owner of Bologna's soccer team has been found murdered, but that investigation - and the motives of the killer - matters much less than all the satirical routines. Dibdin packs in a celebrity chef who can't cook, a ludicrous private eye, more Sellers than Chandler, and a cartoon version of Umberto Eco as a glib donnish superstar named "Edgardo Ugo". Anyone who remembers the melancholic elegance of the early Zens may feel vaguely insulted. You know that a crime writer has lost his way and his zest when a character prattles self-referentially (as "Ugo" does) about "a deconstruction of the realistic, plot-driven novel". In which case, fans might wonder, why not start to deconstruct Dibdin's sales figures too?
Besides, why stick with a pretend Italian when you can enjoy the real thing? Readers who want a native rival to Zen should hunt down The Voice of the Violin, the latest of Andrea Camilleri's fine Inspector Montalbano mysteries to be exported (translated by Stephen Sartarelli; Picador, £12.99). Here, "Italian" counts as an official term: Camilleri is above all a proud Sicilian. His crime novels convey a quiet devotion to the island's people, places and (mouth-wateringly) its food.
This time, Montalbano has to cope with the death of a glamorous incomer who was building her Sicilian dream home, the fatal blunders of the Flying Squad, and a disfigured violin virtuoso who may hold the key to the murder. Camilleri still respects his readers enough to lavish care and craft on plot and clues, while the local colour comes naturally in unobtrusive strokes. The result is that Montalbano's latest course seems as satisfying as the "substantial dish of lamb alla cacciatora" that he puts away. Zen's escapade, in contrast, feels about as nourishing as a slapdash pile of fake "spaghetti bolognese" thrown down with contempt in an English greasy-spoon.