Look at famous examples of narratives that don't use "I." Scores of classic novels are in third person, as are many great narrative works of history and biography. You'll discover that avoiding "I" doesn't necessarily prevent you from injecting your own perspective into a narrative; it just makes it more difficult. Jane Austen is famous for using a technique called "free indirect speech" to allow her characters to express their opinions as if they were using "I" when they aren't. Many of James Joyce's classic short stories, including "Little Cloud" and "The Dead," appear in a third-person style that still gives the reader insight into their protagonists' feelings. Henry Adams calls himself "Adams" and "the private secretary" rather than "I" throughout his autobiography.
Position yourself outside the narrative. If you're writing events that you don't participate in, such as the fall of Rome, avoid injecting your opinion or perspective. If, on the other hand, you're writing about your own life, focus on what people other than yourself were doing in the scene you're writing. For example, if you're writing about your eighth birthday party, refer to people without using first-person subject pronouns -- -such as writing "the old woman" rather than "my grandmother".
Describe everything. One advantage of not using "I" is that, because you don't have to worry about directly reporting your own insights, you can take time to record almost everything else in a scene. Descriptions don't require you to make use of "I." You can rewrite the following sentence "I saw two delicious-looking cakes sitting on a table" as "On a table sat two large cakes covered in pink frosting." Notice that the first is more subjective -- you say that the cakes are "delicious-looking" because you think they are -- whereas the second is more objective. You simply give the cakes' color.