Stream of consciousness books can be very tricky if you are not already familiar with them and a lot of people give up because they find the prose to be too dense for them. If used properly, this method of writing can draw readers in, in ways that no other style can. But, in the hands of an amateur, the ever changing flux of thoughts can be a jumbled, distorted mess. One of the most famous authors to ever use this technique is of course Virginia Wolf and I highly recommend reading her essays on the topic if you have not yet done so already. "Modern Fiction" is one of her best I think. As for actual books, I would once again suggest giving Woolf a try. Her books, Mrs, Dalloway, To The Lighthouse, and The Waves are all prime examples of this form of writing.

You have already received some of the more obvious examples in answers here, so here are a couple of more obscure ones that are still very good.

Beautiful Losers by Leonard Cohen (1993) Even if you don't know who Leonard Cohen is, you have surely heard some of his songs, especially Hallelujah (yes that one from the Shrek movie.) Beautiful Losers received a lot of publicity when it was released because it can be quite sexually explicit at times, but don't let that put you off. The novel has also earned Cohen comparisons to James Joyce, which is high praise.

In Search of Lost Time by Marcel Proust (1922) I'm not even going to attempt to describe In Search of Lost Time here, but I take my hat off to the translator who worked on it. Proust was a French author and In Search of Lost Time was his magnum opus. It spans seven volumes and deals with his childhood experiences. The stream of consciousness style writing is pretty apt for describing memories and Proust was a master at making it feel like you are experiencing sights, sounds and smells with him while reading.