Reading Best of the Best American Poetry, I found this wrenching poem by Rodney Jones about the last days of William Carlos Williams. In the process of looking for it online, I discovered that The Atlantic Monthly has a large archive of poetry read aloud which you can access here.
Pank Magazine where was I found this amazing prose poem on childbirth by Elizabeth Evitts Dickinson, and these two poems by Robin Lamer Rahija in text and read aloud. They have an archive stretching back to 2008.
Thrush Poetry Journal is a site I have been visiting recently. It has lots of great poetry including this one by Tawnysha Greene, as well as an archive going back to 2011.