You can strengthen just about any speech by telling a story. (Highly technical presentations may be an exception.)
I’ve written a lot about storytelling, because I believe stories are so important:
The Importance of Storytelling In Speeches
Two Easy Ways to Introduce a Story
How to Tell Stories of Struggle, Loss, and Failure
The problem is, not just any story will do.
As a matter of fact, a lot of stories are lame or stale or juvenile. They make a speech less effective, not more powerful. And they weaken a speaker’s credibility.
The best stories to tell in a speech are wild.
Here’s what I mean.