The first person—“I,” “me,” “my,” etc.—can be a useful and stylish choice in academic writing, but inexperienced writers need to take care when using it.
There are some genres and assignments for which the first person is natural. For example, personal narratives require frequent use of the first person (see, for example, "Employing Narrative in an Essay). Profiles, or brief and entertaining looks at prominent people and events, frequently employ the first person. Reviews, such as for movies or restaurants, often utilize the first person as well. Any writing genre that involves the writer’s taste, recollections, or feelings can potentially utilize the first person.