Here's a compelling example of telling a story on yourself from Paul Nurse, a Nobel laureate and president of Rockefeller University, whose research in cell biology has helped advance understanding of how cancer cells work. Here, he's telling a story about his own family, an intensely personal story told in a personable way, to which any listener can relate. No spoilers here: You need to listen to the story, a remarkable, funny and very frank recounting, to learn how he spins a true tale.
I'd encourage you to think about a story you can tell in this way, especially if it discloses something about you that's pertinent to your audience. Before you do, it's important to take time to think through how you'll tell the story, what you'll emphasize or omit, and where you'll wind it up, as well as what larger point you want it to underscore. In this example, Nurse skillfully works in mentions of his entire family, from his wife and children (whose family tree project led to a surprising discovery) to his mother, sister and grandparents--a simple way to ensure that any one who plays those roles in the audience will be able to see themselves in his story. That's important given his audience at the World Science Festival which aims to reach non-scientific public audiences. His own surprise and discovery emerge as the tale unfolds, and he draws it together at the end by noting the irony that, while he's "not a bad geneticist, my rather simple family kept my own genetic secret for over half a century."
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UPDATE, July 11, 2009: This post was included in Andrew Dlugan's "Best Public Speaking Tips and Techniques: Weekend Review", a nod I'm always happy to have from his Six Minutes blog--another great read for those of you looking for news, tips and advice on public speaking.