Faulkner's "The Big Woods" is my favorite hunting related literature. Although, it is centered around older southern hunting styles and filled with southern slang, so I'm not sure how accessible it is to someone absent this region. Still I think the section "the old people" is outstanding and his prelude within the work, "Mississippi", is a powerful conservation reminder.
I know this is sort of state specific, but this book about the history of the PA Game Commission was one of my favorite reads. It really illustrates how far we have come in terms of wildlife management and law enforcement. The book itself is kind of old now, but still an interesting read.
I would highly recommend all of capsticks books. Also, probably my favorite book of all time is by Jim Corbett. I don’t know the name off the top of my head but it’s short stories about him hunting man eating tigers and leopards
I always like bringing a Sigurd Olson book on canoe trips and hunting trips. Most of his books are made up of short essays and observations about the wilderness, so its a perfect companion, easy to get through a chapter or essay here and there when you have time. I've worn out one or two copies of The Lonely Land and Runes of the North.
I'll second what Europe wrote, except that I'm not a fan of Jack London's writings. I also like Faulkner's works. Try some of Rudyard Kippling's stuff. Russell Annabel is definitely worth looking into for American hunting/outdoor stories. Capstick is a must read for the African stuff and I like Hunter and Ruark for Africa too. Read some of Patterson's stuff. James Corbett was the go-to guy for sorting out man-eaters in India back when Britain had stock in Asia, he has some good works.