Phantoms in the Brain by V S Ramachandran - a book about how the brain organises itself in bizarre edge cases. The Tell-Tale Brain: A Neuroscientist's Quest for What Makes us Human. The Tell-Tale Brain: A Neuroscientist's Quest for What Makes us Human by the same author is also worth reading.
Admissions by Henry Marsh - An experienced neurosurgeon's account of how his job has changed over the decades. Really interesting discussion of what's important and how people react in a real crisis.
The Man Who Mistook His Wife For A Hat by Oliver Sacks. More of a collection of interesting curiousities but does an amazing job of humanising the discussion of brain.