What makes a good mystery? I think every one has their own idea. Mystery is such a wide-ranging genre and is usually combined with something else: "cozy", Regency romance mystery, police procedural, historical, post-apocalyptic, contemporary New Adult mystery. If you did a double-take on New Adult, you're sharp: it's a new category of 18+ protagonists, no doubt in response to the enormous interest in what used to be called YA (Young Adult) fiction. Think Harry Potter and Twilight, and consider that over a third of YA readers left their YA years behind decades ago. I'd like to think that it's because the books are so compelling, but even author Stephenie Myers has said the Twilight writing wasn't so hot.
Nothing in this post should give you the idea these are the only mystery writers to look for. This is, along with romance, the most popular genre in the United States. While other countries don't gobble up crime in all its permutations the way Americans do, and many citizens of other countries sneer at mystery-toting American tourists, we will happily gobble up anybody's mysteries.
Particularly if they're British. It can be argued that a British writer, Dorothy L. Sayers, with the creation of Lord Peter Wimsy, actually created the genre. The first Wimsey story was set in the 1920's. I believe that one of the best is Gaudy Night. If you are intent on reading the late, great Sayers in strict order, go to Michael Rawdon's personal website and find his book reviews. He has an excellent chronology:  
No, I'm not forgetting the Lady in the Bathtub (which is where she purportedly preferred to write), the incomparable Agatha Christie. Yes, she is good, great, fantastic, but this is a personal blog and I put Sayers a bit higher on the pyramid. You might not; fine.
Sayers would be impossible to emulate. Like all great writers, she's in a class by herself, with a unique and witty voice. (Think Elmore Leonard, Ivan Doig, and all the other writers mentioned here). So, you write in your own voice, which can take a very long time to find. And your plotting has to be impeccable. Your characters unusual but not too weird (unless you're writing slasher fiction). Your setting authentic without taking over. Your social milieu well researched (remember, no beehive hairdos in the 1920's!).
I'm gallivanting through Death by Water, one of the Phryne Fisher series, and you'll never find a better example of beautifully constructed sentences, scenes, and plot. The author - Kerry Greenwood, an Australian - has spent years honing her writing skills. Words are not wasted, what she's published is all that needs to be said. Fabulous! These books are a pleasure to read, not only on the mystery level but the social level: 1928, independently wealthy British woman with exotic Chinese boyfriend, a puritanical maid (oops: companion) named Dot, and all the odd characters and skulduggery you could want.
Greenwood is in the same frame as Edgar- and Anthony-Award winner Rhys Bowen, whose 1930's-based Royal Spyness Series stars Lady Georgiana Rannoch. Georgie, #34 in line for the British throne, is habitually broke and desperate for enough money to live on. Start with Her Royal Spyness, and settle in for a lot of delightful reads.
Another author I just bumped into is Robert Barnard, a multi-talented award-winning British author of A Murder in Mayfair, among others. He not only does stand-alones such as Mayfair, but a series starring a black cop aptly named Charlie Peace. I'll be working my way through Barnard's books this year, and will review them as I finish them.
Mysteries such as Archangel, by Robert Harris, fall into the international mystery/thriller (see what I mean about categories?). This novel has underpinnings from the Stalin era, so purists could also add historical.
Speaking of historical:
Jason Goodwin, whose Constantinople-based series starring Yashim the eunuch are sophisticated and complex. Goodwin is an Ottoman scholar, and the novels are entrancingly dense. Begin with The Janissary Tree; you'll want to gobble up all these tasty tales.
Hyper-productive Barbara Hambly, whose New Orleans-based pre-Civil War series starring black, son of a house slave and and now physician/musician, Benjamin January, will at times make your flesh crawl. January's history, and his present trials and tribulations will keep you entranced. A Free Man of Color begins this series.
Laurie R. King's series (12 and counting?) starring Mary Russell and Sherlock Holmes can only be described as deep, delightful, and chock full of derring-do. I admire any author who can so deftly nail an era, a character, and the historic context. Start with The Beekeper's Apprentice; you'll never want to stop.
Anne Perry is the Victorian angst author par excellence. The Thomas and Charlotte Pitt series are at 25 and still coming. Her William Monk series is equally fascinating. All are solidly grounded in Victoria mores, attitudes, and vices, to the extent that once in a while, some of the dialogue is stiflingly boring. 
The late Elizabeth Peters, whose archeologist heroine Amelia Peabody partners the short-fused, sapphire-eyed "Father of Curses" as he excavates Egypt from the Victorian era to World War I and beyond. Peters, like so many accomplished authors, had an  advanced degree: in her case, she was an Egyptologist in her own right. As you'll see from her website, Peters wrote with many pens. I will miss not having another Amelia Peabody novel to look forward to.
Steven Saylor, writing about ancient Rome in his Roma Sub Rosa series starring the marvelous Gordianus the Finder. Begin with The Triumph of Casear, and read all dozen of these gems. Learn more about the author at
Lauren Willig, creator of the Pink Carnation historical mystery/adventure/spy series, which begins with The Secret History of the Pink Carnation. Talk about writer's envy: Willig apparently created this best-selling Napoleonic-era series while she was going through Harvard Law School! When did she sleep? In 2014, she has three books coming out. Way to go! Her website is
From the sublime to the sometimes totally ridiculous:
Janet Evanovich's numbered contemporary (what are they? mysteries? capers? romps? romances? how-to-wreck-a-car tutorials?) series starring skip-tracing hottie Stephanie Plum and her even hotter pair of boyfriends. I had recently thought this series had run its course, but with #19, Stephanie's back on track.
And now back to the tough stuff:
Carol O'Connell, whose series character, the more-then-slightly sociopathic protagonist NYPD Detective Kathy Mallory (never call her by her first name) will put the reader through the wringer. Now if only Charles would wise up... Begin this series with Mallory's Oracle. If you can figure out her web site, please let me know.
Sara Paretsky's Vic Warshawski keeps putting herself through the wringer, and I've come to the sad conclusion that I can root for this woman just so long before I have to give up. The pattern is so very destructive. Guess I'm getting wimpy in my old age. Paretsky's web site has some great old Chicago photos.

Of course, there are many, many more. I'm reading as fast as I can! Tasha Alexander comes to mind; her exquisite historical mysteries are superb. More on her later, or search this blog for several reviews. I have enjoyed Diana Gabaldon's Lord John spin-offs as well.
And now, on to capers:
When does a mystery become a caper? When John Dortmunder and his crew, creation of the late, great Donald Westlake, enter the scene. There's little romantic in these stories, so I can't lump them in with Evanovich. But they are a laugh a page. For good-humored, solid, no-nonsense fun (as opposed to Stephanie Plum's almost slapstick events), highly plotted, gently humorous, uniquely quirky characters, all with many twists and turns, Westlake is the author to seek out.
Does Eric Garcia belong in the caper series? Do dinosaurs caper? You tell me. Garcia has created, in his dinosaur-as-human protagonist in Hot and Sweaty Rex, Anonymous Rex, and Casual Rex, a very unsusual world. Hard to think you'd believe the dinosaur, but you'll love this off-beat subject and Garcia's deft handling of the T Rex's internal dialogues.
Update May 18, 2013: How on earth could I not have included Louise Penny? Canadian author of the celebrated Inspector Gamache series, Penny's beautiful, deep, at times amusing, always human inspector, with his troubled sidekick, investigate at time hair-raising, at time heart-breaking situations. These are especially compelling because of the human dimension Penny brings to her near-literary writing. Or maybe it is literary; what do you think? Start with A Still Life (US titles are often different than Canadian-published titles) which introduces you to the charming village of Three Pines along with a not-so-charming corpse.
Update November 28, 2013: Not usual to find a stupendous debut novel, but I just finished The Andalucian Friend, by Alexander Soderberg. Translated from the Swedish, this tightly-plotted tale leaves Steig Larsen in the dust.