I second Hot Lights, Cold Steel. It was the book that originally got me thinking seriously about medicine. It alternates between very funny and very poignant, and the author is a natural-born story teller. If I could only recommend one medical book, it would be this one.
When the Air Hits Your Brain is also very good, but a little bit harder to find. You might need some booze or something afterwards, as there are some really, really sad and depressing patient stories.
Others that I've read and enjoyed: Final Exam by Pauline Chen, Brain Surgeon by Keith Black, Intern by Sandeep Jauhar, How Doctors Think by Groopman, Blue Collar Blue Scrubs (by the same guy who wrote Hot Lights, Cold Steel, but about his experience before and during medical school-- also very good, but less medical-ly).