“Fairy tales strengthen the moral lives of children.”
How do you determine which fairy tales are age appropriate?  A good gauge is by the way that the conflict (or “evil”) is depicted and by the complexity of the tale.  Here is a basic guide:

Young Three Year Olds:
little nature stories
simple stories about daily life in the home and garden (these are many times “made-up” from daily life.)

Children under three years old do not just imitate, they explore.  They absorb every aspect of their environment – so stories about their daily life will meet their developmental needs.

Older Threes and Four Year Olds:  They love very simple, sequential stories!  If you are new to telling a fairy tale – these are simple to learn.  My kindergarteners still love these stories.
The Giant Turnip
Little Louse and Little Flea
Goldilocks and the Three Bears
The Mitten
The Gingerbread Man
Sweet Porridge

At this age, the child loves repetition!  They will repeat things over and over!  A story that has a repetitive nature is candy to their ears!  And in fact, is building auditory processing.

Four Year Olds and up: A little more complexity but not too much drama!
   The Billy Goats Gruff
   Stone Soup
Little Red Hen
The Elves and the Shoemaker
The Three Little Pigs
The Pancake Mill
The Wolf and the Seven Kids
Mashenka and the Bear

At four years old, the young child is now aware of conflict on a conscious level.  Stories with simple conflicts and easy resolutions delight their need for order in the universe!  Good wins!

Five Year Olds and up:  Stories can have more challenge with good and evil plus more detail!
Star Money
   Little Red Riding Hood
   Rumplestilskin
   Jack and The Bean Stalk
   Hansel and Gretel
Little Briar Rose
The Golden Goose

Six Year Olds and up: Children at this age are now ready for characters that have suffering in their journey.
Rapunzel
Cinderella
Mother Holle
Bremen Town Musicians

This is by no means comprehensive but gives you a feeling for the kind of stories for each age.