You can always start with National Geographic's
list of 100 greatest adventure books.
Here's a few that are not on that list but excellent (IMHO) reading nonetheless:
My favorite Mt Everest book: Snow in the Kingdom by Ed Webster. Excellent writing and outstanding photos.
The Ice Master by Jennifer Niven. An account of an ill fated 1913 Arctic expedition climaxed by the Captain's 700 mile trek to secure a ship to rescue what was left of his crew.
In the Ghost Country by Peter Hillary & John Elder. Hillary and 2 companions (they all grew to truly hate each other during the expedition) cross Antarctica to repeat the route of Robert Falcon Scott. They finish but they are all physically and emotionally damaged at the end.
The Last Place on Earth by Roland Mumford. A sometimes dry but incredibly detailed comparison of Scott and Amundsen and their race for the South Pole. You'll understand why Scott and his men suffered and died and why Amundsen's men actually gained weight on their trips to the Pole.
Anything written by Joe Simpson. Clearly Joe is near the top of pack when it comes to writing about mountain climbing and its philosophical and ethical intricacies.
Winter World by Bernd Heinrich. A wonderful book on how animals are able to survive winter weather.
The Adventures of Theodore Roosevelt by T. Roosevelt. Excerpts from TR's numerous books on his many adventures out west, in Africa, as a Rough Rider in wartime and in the Brazilian jungle on an uncharted river (The River of Doubt). This guy was very ballsy and an eloquent author to boot.
JohnL