What is a cozy mystery I have been asked on several occasions. Well according to Wikipedia it is: "A subgenre of crime fiction in which sex and violence are downplayed or treated humorously, and the crime and detection take place in a small, socially intimate community." Site Source
To me its sums it up basically, a crime story without the gore and sex. It could even be a ghost story without extreme horror in it, think more along the lines of G rated stories.
Sites That List Cozies By Genre,Time, Place
Cozy Mysteries Unlimited
Cozy Mystery List - Also has an excellent description of what a cozy is
Authors Of Cozies
In No Particular Order
Mystery, Mahem And Intrepid Lady Sleuths