This list will focus on my favourite books about NASA and the American space program.
Apollo: The Race to the Moon
by Charles Murray and Catherine Bly Cox.
If you only read one book about the space program, this should be the one, even though it only focuses on the Apollo program. Its style, brilliance and insight put it head and shoulders above any competitors. Murray and Cox see the space program as a whole, and offer so much more than a bland recitation of mission details. Their book has been recommended by several former flight controllers, and has been used fairly intensively by NASA historians. The website is good too.
The Challenger Launch Decision: Risky Technology, Culture and Deviance at NASA
by Diane Vaughan.
A very insightful and densely written book that cuts through many of the myths surrounding the Challenger accident. Before reading this book, I thought that I understood what had happened to Challenger. I was wrong.
Carrying the Fire
by Michael Collins.
This is the only astronaut memoir that I have any time for (although I haven't read as many as I should). Collins is much more eloquent and reflective than the typical Apollo-era astronaut.
Moondust: In Search of the Men Who Fell to Earth
by Andrew Smith.
At a basic level, this is an account of has what happened to the men who walked on the moon in the nearly forty years since it happened. It is also a very subtle study of how what they did affected them, how it affected all of us, and what the moon landings really meant to the world. This is a very accessible and non-technical book, but I found it stayed with me for a long time.
Moon Lander: How We Developed the Apollo Lunar Module
by Thomas Kelly.
The development and construction of the lunar module, as narrated by its chief engineer. This book hits the perfect balance between autobiography and historical narrative, and between technical detail and readability. It is also very fluidly written. Tom Kelly, sadly no longer alive, was a remarkable man.