My Kindle has a poetry section, and when I go to it, I frequently visit Robert Frost to read Mending Wall or The Road Not Taken. Shelly's Ozymandias made an impression on me in college, and it still does. As long as it is, I come back to Hiawatha by Longfellow, drawn in by its rhythm and story line. Last night I re-read Thomas Gray's Elegy Written in a Country Church-Yard and will no doubt read it several more times during my life. For a long time I kept coming back to his On The Death of a Favourite Cat, Drowned in a Tub of Gold Fishes, mainly for its clever ending. (But if Gray really observed this, why didn't he just save the poor cat?)
Some other poems I've enjoyed that come to mind:
Dover Beach by Matthew Arnold
Howl by Alan Ginsburg
Renascence by Edna St. Vincent Millay
When Lilacs Last in the Door-yard Bloom’d by Walt Whitman
...and pretty much anything by Emily Dickinson
Who are your favorite poets? And when you read a poem to yourself, do you ever read it aloud? I do.