I second Hot Lights, Cold Steel, The Emperor of All Maladies, and anything by Atul Gawande.
I'll add The Immortal Life of Henrietta Lacks, because it shines a bright and uncomfortable light onto how medicine was practiced in the 50s and 60s, how medicine was practiced before the era of informed consent, and the disparities between whites and blacks during that time well into the current day.
I also loved My Own Country, by Abraham Verghese. It's fantastically written and chronicles Dr. Verghese's journey from IM resident to infectious disease specialist, and how he became the AIDS doctor of Johnson City, TN during the years before AIDS had a name or even a source. Even better, he writes beautifully about how he, a foreign medical graduate, found a home and a community to call his own in rural America, of all places. When you read the book, you feel like you're sitting right there with him on the front porches and in the bars, meeting and talking to these patients, neighbors, and friends.
The Emperor of All Maladies, The Immortal Life of Henrietta Lacks, and My Own Country are also great books to share with non-medical people in your life, because they're written to be accessible to people with no medical background. Even The Emperor of All Maladies, and it delves into some pretty dense concepts.
How Doctors Feel by Danielle Ofri is another good one. It's also memoir-styled, but the title sort of explains itself. It's about exactly what it says it's about.
The Man Who Mistook His Wife for a Hat is a fun read as well.