In which fairy tales and which animals said don’t eat me?

The most famous example of an animal saying "Don't eat me!" in a fairy tale is the Gingerbread Man from the Brothers Grimm's fairy tale "The Gingerbread Man". In the story, the Gingerbread Man is baked by an old woman and immediately starts running away from her, screaming "Run, run, as fast as you can! You can't catch me, I'm the Gingerbread Man!"

The old woman and her husband then try to catch the Gingerbread Man, but he continually outsmarts them and escapes. He eventually meets a fox who tries to trick him into getting close enough to be eaten. The Gingerbread Man says "Oh, no, no! I won't come down. I know what you're up to. You want to eat me up!"

The fox then tries to sweet talk the Gingerbread Man, saying "Oh, no, no! I won't eat you. I only want to play with you. Come down and we'll have some fun!" But the Gingerbread Man is not fooled and continues to run away from the fox, shouting "Run, run, as fast as you can! You can't catch me, I'm the Gingerbread Man!"

In the end, the Gingerbread Man is eaten by the fox, but his example of not being tricked into getting close enough to be eaten is an important moral lesson in the story.