It's easy: they invented Lyrical Poetry, which is what almost everyone has written since.
You may have missed the three most influential poets of all; namely, Sappho, Alcaeus and Anacreon. Why do I consider them to be the most influential? It's easy: they invented Lyrical Poetry, which is what almost everyone has written since. Before they began writing personal poetry to appeal to themselves and their friends, poets wrote crap on behalf of monarchs and military leaders in praise of their exploits and deeds. Sappho was the first person to write deeply personal, reflective poems. Alcaeus wrote what are probably the first political poems, while Anacreon wrote poems that celebrated Life and living. The also invented complex meters that poets in later times (including Ezra Pound) would experiment with. The King James Bible is also hugely influential, since it was the first collection of poetry written in Free Verse.