Using a broad, all encompassing definition of "outdoors" here that includes all forms of outside recreation: hiking, camping, horseback riding, hunting, mountaineering, birdwatching, etc. From stories of people who make a living outside (Ranger Confidential), to people who just like to go out on adventures (The Big Year, Pecked to Death by Ducks), to the tragedy that befalls some unlucky few who underestimate Mother Nature (Into Thin Air, Death in Yellowstone), it's all here. These are all required reading for students of Go Outside And Do Things University.
I avoided most scientific books (The Selfish Gene, etc) in favor of books that focus more on the environment as a character, are more narrative-driven, and which place a heavy emphasis on enjoying the outdoors. That said, you will notice some science books on here, mostly conservation-driven ones like Silent Spring or A Sand County Almanac. I made such exceptions since our actions outside impact the natural world we so love.