I used to belong to a literature forum and one of the burning questions there was always, "What is poetry?" The consensus among the forum members was that poetry was determined by beautiful language, but I can't agree with that. If language were the determing factor in what makes poetry poetry, then Edna O'Brien's lush, gorgeous prose would be poetry, and it's not. It's lush, gorgeous, poetic-like prose, but it's not poetry.
First, I think it's important to realize that poetry is the most compressed and unified form of literature, and the lyric poem is probably subject to more rules and constraints than any othe form of writing.
I don't agree that beautiful language makes a poem because a poem, even a great poem, can be constructed from plain, everyday language, e.g., "The Purple Cow" by Gelett Burgess:
"I never saw a purple cow;/I never hope to see one;/But I can tell you anyhow;/I'd rather see than be one."
This is a poem, yet it uses no lyrically beautiful language. It's very conversational. And, like I've already mentioned, Irish novelist's Edna O'Brien's prose is poetically beautiful, but it's still not poetry.
The answer as to what distinguishes poetry from any other form of writing is - patterns. Patterns of sound. The patterns of sound are what distinguist poetry from other forms of literature, what gives the language its music. Free verse has rhythm and patterning, too, they just aren't as obvious or as regular as those found in more formal, lyrical poetry, but the repetitions of consonant and vowel sounds give free verse enough of a pattern to transform it into poetry.
Free verse isn't a twentieth century invention. Anglo-Saxon poetry used repeted consonants and stresses, and phrasing patterns. Japanese and Greek poetry used syllabic patterns, all of which can be found in contemporary free verse.
Many people who write poetry but don't read poetry tend to write "rhyming verse," instead. It rhymes, but the lack of unity usually precludes it from being real poetry. I think these people need to study Federico Garcia Lorca's concept of "duende," - the emotional patterning that turns rhythm and sound into real poetry.
To sum up, I think, and this is only my opinion, it's the intertwining of sound patterns - of consonants, vowels, and rhythm, that makes poetry, poetry. Life is made up of patterns, and poetry, more than any other form of writing, delves straight to the center of life.