A "traditional" mystery whose best-known practitioner is Agatha Christie. Common elements include: a domestic setting such as a country house or quiet neighborhood; a limited roster of suspects, all part of the victim's social circle; little or no description of violence or sex; a mildly romantic subplot; and an amateur sleuth or eccentric professional.There is also often a cat. Contrary to popular opinion, a cozy does not mean the kind of story where the cat solves the crime. That is one kind of cozy and, yes, I have been known to buy mysteries because they have a cat on the cover! I read many different kinds of mysteries but am especially fond of cozies.
The wonderful things about cozies is that there are so many to choose from. Whatever you are interested in, there's a mysteries series for you. There are too many sub-genres to list here but some popular ones are culinary (with recipes), cats, dogs, horses, historical, supernatural, coffee shops, inns, etc. I'm sure you get the idea. The tone of cozies varies as well, so you can always find something to suit your mood (light and funny, serious, scary, etc.).
Where can you find out if you like cozies? I recommend Detecting Women 2: Reader's Guide and Checklist for Mystery Series Written by Women by Willetta Heising. The checklist (by author) are helpful but so is the huge cross-reference section where you can look up series/authors by the sub-genre (culinary, supernatural, historical, etc.). This books is limited to female authors but Heising also has a Detecting Men checklist for male authors (all genres, not just cozies). Unfortunately, Detecting Men does not include a cross-reference section and is limited to authors who write series (so don't look here for authors like Dick Francis).
My favorite bookstore, Aunt Agatha's in Ann Arbor, is a great place to find any kind of mystery. They even have cross reference notes on the shelves ("If you like Anne Perry you might also like Elizabeth Peters, Robin Paige, etc.").
I did a quick Internet search and found Cozy Mystery List with lots of info on cozies and two humorous definitions of cozies: Cozies I Have Known by Polly Whitney and What Makes a Cozy Just That?
What I like about cozies: interesting characters, settings (including places and historical settings like Anne Perry's Victorian England), and plots. I also love the variety of sub-genres. I will read a series just for characters I like, even if it's not "perfect." For example, one of my friends says that Ellis Peters' Brother Cadfael series is nothing like a real 12th century Bendictine monestary, but I don't care. I love the characters so much I can suspend my disblief.
The suspension of disbelief is required to some degree to read any mystery novel with an amateur sleuth but when a story becomes so implausible it destroys that suspension, I won't read or watch it. Some examples: most Agatha Christie but especially And Then There Were None (aka Ten Little Indians) and Jessic Fletcher. Call me a heretic, but I don't like Agatha Christie. I can tolerate Miss Marple on TV but Hercule Poirot needs his fussy little face slapped. I just don't understand why so many people like these characters. And don't get me started on Jessica Fletcher! Most serious mystery fans are sure Jessica is really a serial killer. What else could explain the fact that she stumbles over dead bodies everywhere she goes?
Sure, it's easy to make fun of a badly written traditional mystery (like Jessica Fletcher) but nothing beats a well-written cozy. Be sure to read it on a rainy night while you are snuggling with favorite cat or dog and sipping your favorite beverage. It's a mini-vacation of literary bliss!