Trout by Ray Bergman was probably the most influential book for me, in two ways.
1) The book made flyfishing for trout seem very interesting, so it got me all enthusiastic to do that kind of fishing, even before I was old enough to drive to get to the streams.
2) Bergman was versatile, i.e. he fished dries, wets, nymphs, streamers, depending on the conditions. His book influenced me from the very beginning to think of that as the normal approach to flyfishing, and I still feel the same today.