I loved Aesop's Fables, which were merely parables, such as the Fox and the Grapes, and the Tortoise and the Hare.  I think that since they featured animals they were more interesting to me when I was a kid.  

And don't forget Jesus' parables, such as the Prodigal Son, the Rich man and Lazarus, and the Wise and Foolish Builders.  

The Buddhists have a different spin on the parable that they call a koan. A koan, which translates to fable, is a puzzling, often paradoxical statement, anecdote, question, or verbal exchange, used in Zen Buddhism as an aid to meditation and a means of gaining spiritual awakening. Sometimes it is a story about a Zen master and a student. Other times, it is a riddle with no solution, used to provoke reflection on the inadequacy of logical reasoning, and to lead to enlightenment.

A few examples illustrate how deep this well goes:

• Dizang asked Fayan, “Where are you going from here?”Fayan said, “I’m on pilgrimage.”“What sort of thing is pilgrimage?”“I don’t know.”“Not knowing is most intimate.”Fayan suddenly had a great awakening.
• Linji said, “There is a true person with no rank, who is always coming and going through the portals of your face.”
• The Diamond Sutra says,“Out of nowhere, the heart-mind comes forth.”
• Lingyun was wandering in the mountains and became lost in his walking. He rounded a bend and saw peach blossoms on the other side of the valley. This sight awakened him and he wrote this poem:
  For thirty years I searched for a master swordsman,
  how many times did the leaves fall,
  and the branches burst into bud?
  But from the moment I saw the peach blossoms,
  I’ve had no doubts.
• For twenty years I have struggled fiercely—
  How many times have I gone down to the Blue Dragon’s Cave for you?
  —Xuedou
• A teacher said, “It’s like filling a sieve with water.”
  The student thought about this for some time, but didn’t understand. The teacher took a sieve, and they went to the sea.The student poured water into the sieve, and it poured out again.
• “How do you do it?” she asked.
  The teacher threw the sieve out into the ocean, where it floated for a moment and then sank.

Koans courtesy of the Pacific Zen Institute.