that first came to mind was Western Wind... then as I thought more, I remembered Caedmon's Hymn, which I really enjoy once it's translated from Old English. (And I really enjoy remembering Dr. Hurst from college recite this from memory IN Old English!).
Then there are haiku, which I wonder if they predate the English poetry... I'm not sure because I think haiku didn't start being written until the 14th century.
I suppose I should even go back as far as Biblical / Hebrew poetry, since I know many of the Psalms quite well... that is some old poetry. (and studying Hebrew poetic form is quite fascinating).
I guess I know some pretty old poetry. I like it best.
What's the oldest poem you know?