Start with the classics of mystery fiction -- one can't mention mystery without a bow to the master, Sir Arthur Conan Doyle. Author of some dubiously sci-fi books, his career really took off when he created Sherlock Holmes. Holmes and his sidekick, Watson, live eternally in Doyle's short-story series, as well as his novels, The Hound of the Baskervilles
Of course there's Agatha Christie as well, who created the characters of Miss Marple and Hercule Poirot. I've always loved Miss Marple -- it's so easy to underestimate the scatty old lady knitting in the corner; however, she's nosey as anything and has a wealth of knowledge that no one would imagine her having at all. Christie wrote prolifically, but the quality is a bit uneven. (She was quite mysterious herself; she disappeared at some point during her adult life, reappearing later with no explanation). I recommend as a start Murder on the Orient Express
I've mentioned Dorothy Sayers and her Lord Peter Wimsey before, so I won't get too fulsome here. I'll only mention that The Nine Tailors
Other classic mystery writers include Josephine Tey, who didn't write enough of them to make me happy -- I've reread her Brat Farrar
Not to neglect the American classic mysteries, it's worth trying Rex Stout's
Moving along to our times, P.D. James has, at this point, donned the crown of mystery queen in Christie's place. Also British, her mysteries feature Adam Dalgliesh, who is a far more complex character than any ever created by Christie. James, I think, is really a very sophisticated writer who has chosen to write mysteries. Sometimes a bit horrifying, her stories are the kind that keep you guessing, but not wildly.
I also like Robert Parker's books, which are not too complicated (anyone can pretty much solve them by the end of the first chapter) but are a delight to read. The dialogue is hilariously written, and by the end of the book the reader thinks Spenser is a real person. Last time I went to Boston I looked for him every time I saw someone walking a large black dog (in the books she's called Pearl). Sadly, he died recently, so you'll have to make do with what he's written already. Another similar writer is Bill Pronzini, whose Nameless Detective
This weekend I read Martha Grimes's latest, Fadeaway Girl. I really prefer her Richard Jury series, but she's such a hoot to read that I enjoyed it anyway. Grimes creates terrific characters -- each one has bizzare idiosyncrasies. One doesn't read Grimes for the mystery; I think her books are more about the process. Fadeaway Girl is the sequel to Belle Ruin, and is narrated by a twelve-year-old girl who works in her mother's hotel. Among other responsibilities, she mixes novel cocktails for her Great-Aunt Aurora, who lives on the top floor. Oh, and there are two characters, brothers called Ubub and Ulub (after their license plates -- don't ask) with speech impediments. If you like Grimes, you're lucky -- she's written a lot of books.
A new mystery series I've gone through recently features Flavia De Luce, a ten-year-old growing up in '50's Britain who makes her debut in The Sweetness at the Bottom of the Pie. No, it's not for children. Flavia plays with chemicals as a hobby. There are at least two more of these by Alan Bradley, and he seems to be on a roll.
I'll stop here, because otherwise I could go on all day, but if you have comments, questions, or special requests, please post in the comments section. Also, try to think of any contributions you could make to my Guilty Pleasures post!