Note: Arcanum has a good list of all readings Brandon's done, and the 17th Shard has a good list of all samples of any of his works, so check them out if that's what you're after! The scope of this post is slightly different than either of those, as its goal is to be a list of all Brandon's unpublished books specifically without other things distracting from that aim (and admittedly also to give this instance some starter content :P).
Full Books
These are early works (mostly) from before Brandon got published that are available in their entirety.
- The Way of Kings Prime: Full novel with prose download, audio download, and audio streaming options.
- Mistborn Prime: Full novel you can request through Brandon's contact form. Fill it out and his team will email you a copy (can take a couple weeks depending on load).
- The Aether of Night: Full novel you can request from this 17th Shard thread. Leave a comment and the fine folks over there will DM you a copy (can take a couple weeks depending on load).
- Mythwalker (Warbreaker Prime): Unfinished novel posted to Brandon's blog.
- The Traveler: Short story read aloud in its entirety. (The only one on this sub-list written after he was published.)
- Centrifugal: Short story posted to Brandon's blog.
Samples of "Prime-era" Books
These are early works from before Brandon got published that are available in bits and pieces only.
- Dragonsteel Prime:
- Chapter 1
- Start of Chapter 14
- Bridge Four sequence (Chapters 25, 28, 30, 31, 33, 35, & 37)
- Technically the full novel can be found at Brigham Young University's library, but practically speaking most people can't just pop over there even if they do allow non-students to come in.
- The Liar of Partinel:
- The Final Empire Prime:
- The Sixth Incarnation of Pandora:
Samples of Upcoming/Potential Books
These are samples written after Brandon got published that have not themselves made it into any book as of yet. Most were simply individual test scenes, although a few have full stories attached that nonetheless haven't been released for a variety of reasons.
† marks works currently planned as part of the Cosmere.
- Sixth of the Dusk sequel†:
- Kingmaker†:
- The Silence Divine†:
- The Apocalypse Guard:
- Adamant:
- I Hate Dragons:
Full Drafts of Published Works
While Brandon does readings of a chapter or two for a lot of books, there are a few whose full rough drafts have been made available.
- White Sand: Original prose that adapted into the graphic novel. You can get it by signing up for Brandon's newsletter; once you confirm your email it will send you the latest edition, which includes the download link.
- Warbreaker: For this book, Brandon experimented with releasing each draft as he wrote it. You can find a list of all versions on his website.
There is one other story I know of which has been partially released, The Eyes (a precursor to Skyward), about fifteen pages of which were posted to the Writing Excuses Patreon. However, in addition to feeling kind of iffy about pointing people to paying $10 for a very small sample from a very rough draft, the tier the file was attached to does not actually exist anymore, so I'm not sure whether subscribing even will give it to you now or not. As such, I've left it off the list.