Murder She Wrote, but actually written (although sometimes it's hard NOT to picture Angela Lansbury while reading a cozy). Anything violent or bloody takes place "off stage", and the person that solves the crime is usually not in the crime solving workforce.
Agatha Christie and that is where I got my start and my love for mysteries (that and playing Clue numerous times as a kid). We got our first VCR in 1983, and I vividly remember our Sunday afternoons with fresh popcorn and a movie together as a family (it was usually the one day that my dad was home). Those movies were either a musical or one the the BBC Agatha Christie movies (okay an occasional western was thrown in there for dad). I first picked up Agatha to read when I was in junior high and my grandmother was first diagnosed with cancer. Sitting in the hospital lounge for a week because I was not old enough to be on the ward with her for more than short visits, reading Agatha and trying to figure out who did it before Miss Marple is what got me through that summer. The books were borrowed from my grandmother's apartment, so reading something she liked made me feel closer to her. I preferred the more exotic ones- Murder on the Nile, The Man In the Brown Suit, They Came to Baghdad, A Caribbean Mystery. In fact when I got to go to Egypt, I kept thinking "this is where xyz happened in Death on the Nile"... our boat even looked like the one in the movie, I was in heaven!
Laura Childs' Tea Shop cozy mystery series. I had not picked up a pleasure book in about 2 years, but I was on vacation and what better place to buy a tea shop book than in the tea shop. I read the first book that day and night. I was hooked again on the genre. When we got home, I went back to my high stress job teaching, he went back to working in fast paced lobbying, and we didn't see our child from 7am to 7pm. We knew we needed to change our lifestyle, and I kept going back to the tea shop series (and then moved on to the Goldy Bear Catering series by Diane Mott Davidson). I kept thinking about these two women that owned their own small business in a small town (well, Charleston is not small, but Thea's world there is). I actually spent hours looking up teas and tea suppliers thinking that a teashop would be perfect. I went from that to a B&B (could use all those great recipes from the books). When we started looking for a place to move to to get out of the rat race of DC we looked at Lancaster County with an eye for buying a B&B... instead we opened a bookshop, fully inspired by the hominess of Thea's Teashop in the Childs books.
Monica Ferris. I learned how to knit thanks to Maggie Sefton. I plan days of baking thanks to Joanne Fluke, Laura Childs et al. Cozies give me an escape to be with a character that I sometimes think, "that could be me!" Minus the murder, I think cozy mysteries are some of the most realistic and relatable books being written today.