I recommend John Dickson Carr/AKA Carter Dickson.
Not only was Carr the master of the locked room mystery, his elaborate puzzles are wickedly difficult and clever. And unlike many an Agatha Christie mystery, identifying the murderer is very challenging.
I particularly like **The Judas Window, The Problem of the Green Capsule, ** and The Red Widow Murders.
If you have not read The Murder of Roger Ackroyd, you need to, immediately. The best mystery of its type of all time. All the wonderful conventions of English drawing room mystery, and (shakes finger warningly) if you are one of those people who reads the last page to see how it comes out, you deserve whatever happens to you!
The Maltese Falcon isn’t exactly a mystery, since nobody really cares all that much who committed the central murder of the plot, but one of the ten best novels of all time nonetheless.
Anything by Dick Francis is good. I care nothing whatever about horse racing, but darn he’s good. More classic stuff? Any Raymond Chandler. Start with Lady in the Lake or Red Wind.
I wouldn’t take Annie X-Mas’s word for it on Sue Grafton. 
Regards,
Shodan
Go get the Father Brown Omnibus. I think it comes in three volumes.
The Judge Dee mysteries by Robert Van Gulik
Read a mystery, & learn about the golden age of China.
For something a bit lighter, you might read J.A. Jance. She has two sets of novels. The ones set in Arizona with Joanna Brady are my favorite. She also has a series featuring J.P. Beaumont in Seattle. They’re great summer light reads.
Kate Shugak series by Dana Stabenow. Set in Alaska, with lots of detail about bush life. Start with A Cold Day for Murder.
Southern Vampire series by Charlaine Harris. Cocktail waitress with vampire boyfriend in rural Louisiana. The first book is Dead Until Dark.
Kay Scarpetta series by Patricia Cornwell. Medical-legal stories set in Virginia. The first one is Postmortem.
In Death series by J. D. Robb. Sort of near-future SF. Start with Naked in Death.
Spencer Arrowood series by Sharyn McCrumb. These have an Appalachian folk-story feel to them. The first one is If Ever I Return, Pretty Peggy O.
Elizabeth MacPherson series, also by Sharyn McCrumb, starts with Sick of Shadows. The main character is a forensic anthropologist/archaeologist.
Nina Reilly series, by Perri O’Shaughnessy. Legal-themed stories beginning with Motion to Suppress
All these should be read in order, since some of the earlier books are referenced in later ones.
A nice resource is Stop, You’re Killing Me. You can browse by author or character name, and many of the titles are linked to amazon.com. There are links to authors’ websites, too.
Yeah, I read a lot of mysteries.
[hijack] Lynn Bodoni, are you reading Too Many Cooks? I still can’t read that one without cringing. [/hijack]
If you’re interested in the genre-within-a-genre that is medieval mystery, go for Ellis Peters’ Brother Cadfael books or Margaret Frazer’s Sister Frevisse mysteries.
Since the OP wanted to avoid violence, I would definitely recommend against Andrew Vachss and Patricia Cornwall. Good, but very violent.
I second, third, whatever the Dorothy Sayers recommendation. Murder Must Advertise was a good one.
Also really enjoy Lawrence Block, and the Bernie Rhodenbarr series is very good. Matthew Scudder series is quite dark.
Diane Mott Davidson’s and Janet Evanovich write “kinda” mysteries that are light and cheerful.
I would also recommend Barbara Hambly’s Benjamin January books, if historical mystery appeals. These are set in New Orleans and are very well researched.
Lots of good suggestions here.
Josephine Tey is also very good-if one likes British mysteries (no violence at all, really). Start with Brat Farrar…sadly, there are only 5 (7?).
Georgette Heyer also wrote some good, solid mysteries.
Ruth Rendell is excellent, and a bit more up to date.
PD James is good, as is Sharyn McCrumb–I like her appalachian series best.
MC Beaton is good for a quick fun read-there’s not much to them. Her Agatha Raisin series is also good.
Elizabeth George is good, but she should be read in order, and I dont’ recall the first in the series.
the local library should have lists of “if you liked this mystery, you’ll probably like…”
I tend to prefer British, series, Golden Age (either between wars or just after WW2).
Agatha is great–I prefer Miss Marple and Poirot–dont’ care for Tuppence and Tommy or Harlequin.'s
Simon Brett is good.
Margaret Yorke is too.
Minette Walters is excellent, contemporary, but also a bit more violent.
There are many more authors that I just cannot recall at present.
If you like a little humor with your mystery…
Joan Hess.
Her Maggody series.
My favorite mystery author is Raymond Chandler. Square in the ‘Hard Boiled’ detective fiction category, but excellent reads, especially ‘The Long Goodbye’ and "The Big Sleep’.
Robert B Parker has taken up the theme of “down these mean streets a few good men must go” in a modern context. He’s even finished a manuscript Chandler left, and has written a sequel to ‘The Big Sleep’ called “Perchance to Dream”.
Occasionally violent, but never gory for it’s own sake.
Anything by Michael Connelly, especially the Harry Bosch series. Also check out the Lincoln Rhyme series by Jeffery Deaver.
Good Egg, if you liked Dave Barry’s book, you must check out Donald Westlake. He did it first, and better, and cleaner, and he has written a lot of books, so you won’t run out soon.
The man has taste. These are 2 of my favorite authors.
If you want something funny try **Anne George **.
Eliabeth Peters is always a good read as is Earlene Fowler.
Jo Dereske does a funny series about a Librarian.
Tamar Myer does a great amish series.
Did anybody mention Diane Mott Davidson?
I’m currently rereading Georgette Heyer she wrote alot of romance books but only 11 mysteries. They’re from the 30’s and 40’s and a great read.
If you want more medieval mysteries, try the Catherine LeVendeur mysteries by Sharan Newman. Medieval France, with special appearances by Heloise and Abelard. Sharan Newman is very knowledgeable about medieval life/history/what-have-you, and wrote a book debunking The Da Vinci Code. I’m itching to get my hands on it, but my library system doesn’t have it. 
She really is a better author than Dan Brown, if only because she knows how to research and draw believable conspiracies.
Also try The Name of the Rose by Umberto Eco. I’m reading it now after having watched the movie about four times in the past week, and I’m wondering where they’ve been my whole life. Amazingly, I’m not cringing at either the movie or the book yet. It’s not really a mystery in the beach-reading sense, but fantastic nonetheless. There’s some non-translated Latin, though, which might be offputting for some. It’s mostly book titles and some quotations, but they’re all found easily enough online or puzzled out on your own for the gist of it.
I have some Candace Robb waiting for me, as well. She comes highly recommended to me from a previous thread.
Let’s see…I second the recommendations of:
[ul]Elizabeth Peters, especially the Amelia Peabody series, which is about a family of British archeologists (1884-1922 - so far). Read them in order. I think I’ve read one of the Vicky Bliss novels and maybe one of the non-series ones, but I really like Amelia and her family. I wouldn’t read too many of them in a row though. I read about 5 last summer (a couple were re-reads) and it got to be too much.
[li]Dana Stabenow, who has two series that I’ve read: Kate Shugak and Liam Campbell. Here’s a link that takes you to links to all her series. [/ul][/li]I’ve read and liked many of the authors mentioned (Diane Mott Davidson, Joan Hess, Laura Lippman, Janet Evanovich, Dorothy Sayers, Robert B. Parker, Sue Grafton).
A couple I haven’t seen mentioned, who are among my favorites:
[ul]
[li]Margaret Maron - Both the Deborah Knott and Sigrid Harald series. [/li][li]Marcia Muller, who’s Sharon McCone series has become more compelling - I think - with each book. Her complete bibliography is at the bottom of this page[/li][/ul]
I agree that you’ll probably find Patricia Cornwell too violent. There are lots more…and now I have to go take a look at some of the authors mentioned here whose books I haven’t read.
GT
A couple of my favorites:
Ellis Peters, who writes about Brother Cadfael (also done as a good PBS series with Derek Jacobi), a medieval monk. The first book is A Morbid Taste for Bones; IIRC they can be read out of order.
Steven White, who writes psychological mysteries about his main character Alan Gregory. The first book is Private Practices, but while the later books reference situations in earlier ones, they DO stand alone.
Also, Jonathan Kellerman is VERY good, particularly his Alex Delaware books (first one is When the Bough Breaks) but he might be a little too violent for you.
I’d concur with many of the choices, particularly on the Agatha Christie.
Hope this helps!
You might want to try to find a copy of Search the Seven Hills by Barbara Hambly, then. It’s not her best work, but it’s a mystery set in ancient Rome.
Yep. I had to set it aside for a couple of days, because I was getting aggravated about it. At least Wolfe, if nobody else, treats the blacks with dignity and respect.
There have been a couple authors mentioned that I couldn’t finish because they were too gross for me. Cornwell is way beyond me. The writing and plotting might be good (I can’t really say. Never got that far), but the autopsies? No thank you!
I also couldn’t read Connelly, Stabenow, or most of Deaver.
I want to second the Margaret Maron and Sharyn McCrumb and Margaret Frazer and Sharan Newman and Tamar Myers. Lots of good stuff. Maron and McCrumb are perhaps more atmospheric than enthralling, and Frazer and Newman might be extremely boring if you don’t share my fascination with medieval life. I still haven’t read Ellis Peters! hangs head
Ellis Peters is very good.
tinkertoy --I lurve Georgette Heyer’s mysteries. (and her Regency novels-they are the only “romances” that I like).