Among the many poetic and literary examples of stream-of-consciousness writing, perhaps the most famous are Virginia Woolf's Mrs. Dalloway, a novel that follows Clarissa Dalloway throughout a single day in London, using stream of consciousness to reveal her thoughts, memories, and perceptions as she prepares for a party, and James Joyce's Ulysses, considered a landmark work of modernist literature. Ulysses employs stream of consciousness to explore the inner lives of Leopold Bloom, Stephen Dedalus, and Molly Bloom over the course of a single day in Dublin.
William Faulkner, Marcel Proust, Dorothy Richardson, and Samuel Beckett are also considered masters of the style.
I have employed Stream of Consciousness in my poetry before but I am as a babe in the woods compared to the luminaries above.
For a good example of "streaming" read Molly Bloom’s final words (Ulysses) –the last words of the book.