How can poetry that doesn't rhyme be so pleasing to the ear?

Without form, meter or plot, Dylan Thomas' Under Milk Wood, a 'play for voices,' is my favorite work of epic poetry.

Richard Burton leads the first, and best, recorded performance: http://www.youtube.com/watch?v=xy0srtmv3og&feature=&... - but at two hours, you may want to wait rather than interrupt it once begun.

I would argue that the lyrical quality of poetry comes from the meter and cadence of the words, and not from rhyming. Personally, rhyming poetry sounds goofy to me. Without meter, it's just flat prose. Although I'm sure a good speaker (e.g., Morgan Freeman) can make flat prose sound "poetic"

Answer: Have Morgan Freeman read it.

Rhyme is but an ornament, hung from the branch of a greater, elemental thing.