I'm asked on almost every trip to recommend a reading list. Here is the stack that I pull from regularly:
These first three books cover everything I ever do in the mountains. They're a much more comprehensive and understandable collection than the Mountaineer's Freedom of the Hills.
Alpine Climbing: Techniques to Take You Higher, by Mark Houston and Kathy Cosley.
Backcountry Skiing: Skills for Ski Touring and Ski Mountaineering, by Martin Volken, Scott Schell, and Margaret Wheeler.
Climbing Self Rescue: Improvising Solutions for Serious Situations, by Andy Tyson and Molly Loomis.
These next two books are a little dated (Extreme Alpinism was printed in 1999 and Self-Rescue in 1997), but are still worthy reads. Twight's book inspired me to examine my climbing tactics and strategies. Fasulo's book features the great illustrations of Mike Clelland - I look at the pictures more than read it!!
Extreme Alpinism: Climbing Light, Fast, and High, by Mark Twight.
Self-Rescue, by David Fasulo.