You're talking about "stream of conciousness." That's so art nouveau.
I have milk crates filled with notebooks filled with streams of conciousness from when I thought every little thing that crossed my mind or happened to me was important enough to write down, including writing it down. When I read it now I can find a few things that migh be worth reading... after sifting through all the notebooks filled with dissecting every pathetic detail of breaking up with some girl, eating shrooms, or how lazy I was (I thought I was "depressed." That would've been so much cooler).
If it's worth reading I just call it poetry, or maybe prose poetry, only because I was to lazy, depressed, or high to use grammar.
William S. Burroughs and Rainer Maria Rilke (among others) do an exquisite job of what you are talking about. Try reading Burroughs' Queer, Junkie, and Naked Lunch, in that order. You won't find any freestyle writing in the first two but they set you up with what you need to "get" Naked Lunch (Burroughs' letters to Ginzburg and Kerouac dring the 50's and 60's are a great resource, as well; entire sections of Naked Lunch were simply copied from his letters to Ginzburg) And then read Rilke's only novel, The Notebooks of Malte Laurids Brigge... a world apart from Burroughs, but like minded nonetheless.