I can echo #4 in the recommendation of "Shooting an Elephant". I just taught that for the first time and both I and my students greatly enjoyed it! It is based on George Orwell's experience of colonialism first-hand in Burma and features - you've guess it - an elephant that suffers a rather nasty end.
I always enjoy "Salvation," by Langston Hughes, which is excerpted from his autobiography, Another is "Sister Monroe" by Maya Angelou, also excerpted from one of her larger works. Two others I really appreciate is Mark Twain's "The Mesmerizer" and George Orwell's "Shooting an Elephant." All of these narrative essays are widely anthologized and easily found. Enjoy!
Look into some of Benjamin Franklin's writings and some of the other Colonials. Before the American novel appeared on the scene, essay was the medium through which many of the Early American writers recorded their thoughts. Don't forget the great essayists, Ralph Waldo Emerson (Nature and Self-Reliance) and Henry David Thoreau "Solitude" in Walden).
Or, try the slave narratives, such as The Interesting Narrative of the Life of Olaudah Equiano, or The Narrative of the Life of Frederick Douglass, a Slave, or Gustava Vassa, the African.
One of my favorite examples of a narrative essay comes from The House on Mango Street by Sandra Cisneros. If you follow the link below you will find an excerpt from it called "My Name." I've used this in my writing class as an introduction to essays for a number of reasons.
As an essay, this example does several things well. First, though it does not follow a traditional structure (ie: five paragraphs, intro, body, conclusion) it does not lack organization. There is a definite progression from beginning to end. Though you do not see "first," "next," nor "in conclusion" it transitions logically and smoothly from one idea to the next. This essay does not directly state its thesis, but it certainly maintains a focus on a topic and is cohesive. There is a very definite voice and though the tone is personal, it also is commanding.
In addition to being a well-written essay, there are a few characteristics that makes this example a narrative. First, it utilizes story telling to make its point. Esperanza talks of her father, grandmother and sister as an avenue to really discuss who she is and to reveal a personal glimpse into her heart and life. It also utilizes a few unconventional grammatical techniques, such as run-on sentences and fragments. Stylistically both are acceptable for the narrative mode. Finally, it utilizes figurative language more often than typical persuasive and expository essays. Again, this is a style point that is typically associated with narrative writing.
Whatever your specific assignment happens to be (whether it is a direct prompt or something a little more open), I encourage you to read through this example and consider how you could also employ some of the strengths it displays in your own writing. Have fun. Narrative essays are my favorite.