The following is a list of poems that most speakers of American English know very well, primarily because of their historic, cultural, and linguistic (i.e. many well-known expressions in common use today originated therefrom) importance:
“No Man is an Island,” which is the penultimate paragraph of “Meditation #17”/Meditation XVII from Devotions upon Emergent Occasions (1623-24) by John Donne (1572-1631), who was an English poet and a cleric in the Church of England;
Paul Revere's Ride (1860) by Henry Wadsworth Longfellow (1807-1882), who was an American poet;
Casey at the Bat: A Ballad of the Republic Sung in the Year 1888 (1888) by Ernest Lawrence Thayer under the pen name “Phin” (1863 – 1940), who was an American writer and poet;
I’m nobody! Who are you? (1891) by Emily Elizabeth Dickinson (1830 – 1886), who was an American poet;
In Flanders Fields (1915) by Lieutenant Colonel John McCrae, MD (November 30, 1872 – January 28, 1918), a Canadian poet, physician, author, artist, and soldier during World War I, who died of pneumonia near the end of that war;
Harlem aka A Dream Deferred from Montage of a Dream Deferred (1951) by James Mercer Langston Hughes (February 1, 1902 – May 22, 1967) who was an American poet, social activist, novelist, playwright, and columnist.