So, many many months after Goodreads released their iPhone app, we Android users have one too!
It's a pretty light app, you can look at parts of your profile mostly the top part. Of course you can access your shelves, search for books, and add books. The book pages also have abbreviated page styles.
Most notably, the barcode app hasn't been integrated so it will be hard to add books by just scanning (which is available on the iPhone app).
It's nice to finally have an official app though ^.^ which can update your books, and help you check up info on books more quickly on the Android without having to specifically sync the lists as with some of the other third party apps.
Check out the official announcement, and here's a link to the actual app page.