Continuing (in prose!): Shakespeare's plays are written in "blank verse." (Almost) every line in them has a regular meter, "iambic pentameter." But they are not poems, they are plays. They are plays written in verse.
Carl Sandburg's "The People, Yes," and Walt Whitman's "Song of Myself" are poems. So are many parts of the customary English translations of the Bible, such as the Psalms. They are poems because they are complete literary works--with a beginning, and end, and a title, and because they produce emotion through the use of words in strange ways, and through sound. They express more than the meaning of the words--but they aren't in verse at all.
Here's an example, from Walt Whitman's "Song of Myself." This is part of a poem, but it is not in verse.
I think I could turn and live with animals, they are so placid and self-contain'd,
I stand and look at them long and long.
They do not sweat and whine about their condition,
They do not lie awake in the dark and weep for their sins,
They do not make me sick discussing their duty to God,
Not one is dissatisfied, not one is demented with the mania of owning things,
Not one kneels to another, nor to his kind that lived thousands of years ago,
Not one is respectable or unhappy over the whole earth.