One great Dudley Dursley story is when he finally realizes how mean he has been to Harry Potter. It shows his growth as a character. For example, in the later parts of the series, Dudley starts to see Harry in a different light and even shows a bit of kindness, which is a big change from his bullying ways at the start.
Another good Dudley Dursley story is his reaction when Harry is about to leave the Dursley's house for good. Dudley is hesitant and seems to have mixed feelings. He has grown up with Harry in a strange sort of co - existence and this moment shows that there is more to their relationship than just animosity. It's a complex moment that adds depth to Dudley's character.