Link of the Random Interval of Time (LotRIoT): librivox.org.
LibriVox is the go-to site for free, public-domain audio books (and shorter works). I’ve been listening to a selection of poetry on my daily commute: Blake, Dickinson, Shakespeare and others.
The readers are volunteers, and my gratitude to them is tremendous, but they vary in competence. Some read mechanically; some in sing-song; some melodramatically; and some with the right amount of expression, but with odd choices in emphasis and phrasing. (I have a theory about this last group: I believe they are good prose readers, who give too much semantic weight to line endings when it comes to verse.) Not a few, however, get it just right. What’s more, many of the offerings on LibriVox — especially the shorter ones — are provided in multiple versions with different readers, so you can choose the one you like best. (I suggest someone with a cockney accent, when possible, for Blake’s poems.)
LibriVox provides audio files in mp3 and ogg vorbis formats, and links to text versions of the works. The site can be hard to browse, just because of the sheer number of files in their catalog. Since all offerings are public domain (as are the performances), new works are scarce. With the wealth of classics at your earbuds, though, that’s hardly a problem worth whining about.