Great ideas in this thread. I agree that showing who you are through recounting a personal episode helps the writer to write in his/her own voice and often to stand out in a sea of applicants. The topic doesn’t have to be specifically about an EC, service project, favorite class, etc. My kids wrote about a bad haircut, struggling to clean the popcorn machine at the local cineplex, and being squashed in the standing room section at a performance of “The Tempest.” You can show who you are in your perceptions of everyday events, your word choice, what you include and what you don’t.
You can also write a great essay about what you want to do with your life or how it felt when someone you love died; just know that many other writers will address the same topics in their essays.
The single best suggestion any of my kids ever got about writing, whether a personal essay or an academic paper, is read it to yourself out loud when you’re finished. ETA: Just noticed that @mathmom beat me to this suggestion above! I think she’s right.