A lot of poems are about identity, but some of my favorites are by Langston Hughes, Walt Whitman, and Emily Dickinson.
Hughes' poem "Theme for English B," ostensibly written as a homework assignment for an English class, is a playful meditation on what the young black American man is and is not. Whitman's "Song of Myself" and Dickinson's "I'm nobody. Who are you?" are two very different poems about the speaker's self; Whitman's is expansive and eager to include everything within himself, whereas Dickinson's seems modest but playfully interested in smaller, meaningful friendships or communities.
There are several good and mediocre poems about identity on the web. I have listed the site called "The Poetry Hunter." The site allows one to locate poems of a specific nature. Many of the poems about identity are more modern expressions relative to one's search for identity or one finding one's identity.
One significant poem that comes to mind is "The Road not Taken" by Robert Frost. In the poem the man is looking back on the choices he had to make in his life and who he became because of the road he did not go down (the choices he made that were different).
Some others are: I'm Nobody Who are You, Alone by Maya Angelou, and As I grow Older.