Do you need to put a comma after every line in a poem?

No, you don't. Poems is a very creative way of writing, and therefore punctuation is not needed. However, a lot of poets use punctuation to make sure that the reader is reading the poem the way the poet wants them to.

Another answer:

You need punctuation in a poem where the sense requires it, as with any other genre of writing. To say that poems are 'a very creative way of writing' and 'therefore' do not need punctuation is seriously to misunderstand how language works and what the function of punctuation is. Punctuation is not the enemy of creativity, it is one of the elements that contribute to it. Read Shakespeare, Yeats, Eliot, Milton, Dickinson ... any great poet. You will certainly not find that their work consists of streams of unpunctuated Words; their mastery of the language includes mastery of punctuation as much as mastery of vocabulary and syntax.