The website of one of my favorite books of poetry to browse on rainy days (and least favorite to try and lug around), The Norton Anthology of English Literature, has a few dozen audio samples of poets reading from from their own work, and others'.

The 20th century is represented by poets like W.H. Auden ("Musee des Beaux Arts"), Eavan Boland ("That the Science of Cartography Is Limited"), Ted Hughes ("Pike"), Philip Larkin ("Aubade"), Edith Sitwell ("Still Falls the Rain"), and Dylan Thomas ("Poem in October").

There are also examples of poems from other periods to have a listen to, including the Middle Ages (Seamus Heaney reading from Beowulf), the 16th and early 17th centuries, the Restoration and 18th century Romantics, and the Victorians.

While I'm at it, check out this page of poems at the BBC: Poetry Outloud.