There's the story of 'The Golden Touch' by Nathaniel Hawthorne. King Midas loves gold so much that he wishes everything he touches turns to gold. At first he's overjoyed, but then he realizes he can't eat or drink as even his food and water turn to gold. It has the moral that excessive greed can lead to self - destruction. And also 'The Lion and the Mouse'. The tiny mouse helps the mighty lion who was trapped, showing that kindness is never wasted no matter how small you are.
Sure. One is 'The Boy Who Cried Wolf'. It teaches the importance of honesty. A boy keeps lying that there is a wolf attacking the sheep. When a real wolf comes, no one believes him. Another is 'The Tortoise and the Hare'. It shows that slow and steady can win the race. The overconfident hare takes a nap during the race while the tortoise keeps going and reaches the finish line first.
The story of 'The Ant and the Grasshopper' is a great moral short story. The ant works hard all summer storing food for winter while the grasshopper just sings and plays. When winter comes, the grasshopper has nothing to eat. This story teaches us about the value of hard work and planning for the future.