Most of the books and maps on this page I own and have found useful. Some are focused on Virginia, where I live, as well as nearby states. In no particular order…

Production Fly Tying by A. K. Best – Dense book, every paragraph is packed with detailed tips that make you think, “huh, never thought of that and I’m going to try it right now!” A phenomenal reference by possibly the best dry fly tier there is.
Trout Bum by John Gierach – If you’re going to do this fly fishing thing right, read this classic by one of the best writers in this genre. My other favorite might be Where the Trout Are All as Long as Your Leg, if you really forced me to pick another favorite… all of his books are wonderful.
Trout Streams and Hatches of Pennsylvania; A Complete Fly-Fishing Guide to 140 Rivers and Streams by Charles Meck – Great guide to a bunch of streams in Pennsylvania by the creator of the Patriot dry fly. See also Mid-Atlantic Trout Streams and Their Hatches, another useful Meck reference focusing on some lesser-known spots.
Tying Dry Flies: The Complete Dry Fly Instruction and Pattern Manual by Randall Kaufmann – Get the spiral bound version if you can find it. Excellent photography and very detailed instructions from a master tier and the creator of the Stimulator.
Fly Fishing Virginia: A No Nonsense Guide to Top Waters by Beau Beasley – Good places to fish in Virginia, including some good brook trout waters. See also his Fly Fishing the Mid-Atlantic.
Orvis Fly-Tying Guide by Tom Rosenbauer – Tom is adept at writing about how he ties a variety of classic flies. A very approachable fly tying guide for novices and advanced tiers alike.
Fly-Casting Fundamentals: Distance, Accuracy, Roll Casts, Hauling, Sinking Lines and More by Lefty Kreh – For when you’re away from the small streams and really need to cast. Lefty’s natural body movement technique will allow you to do that effortlessly until you’re old and gray. I don’t actually own this one, but I’ve leafed through it and own several other books by Lefty, all excellent.
The Complete Guide To Eastern Hatches by Tom Fuller – Indispensable reference for identifying and matching hatches in the Eastern U.S.
75 Hikes in Virginia’s Shenandoah National Park by Russ Manning – I consult this book frequently before I head out to the park. But I also carry official ATC Trail Maps when I’m hiking and fishing (for example, the Shenandoah National Park Map – Central District).
Virginia Atlas & Gazetteer – I keep one of these in each car, and have others for Pennsylvania, Maryland/Delaware, West Virginia, and more to come. Useful when you’re in the boonies with no cell phone signal. Mark it up with your favorite spots so you can find them again.
The Complete Book of Fly Tying by Eric Leiser – A little dated perhaps but a classic, with detailed techniques and specific instructions for a variety of classic flies. It starts with a wonderful forward by the late Jack Gartside, one of my favorite fly tiers.
Fly-Fishing the 41st by James Prosek – Have you ever thought that traveling around the world along the 41st parallel in search of undiscovered native trout would be a cool adventure? Prosek has done it.
Trout of the World (reissue) by James Prosek – Beautiful watercolors and text based on his travels around the world in search of trout.
Upriver and Downstream: The Best Fly-Fishing and Angling Adventures from the New York Times – Short pieces from various authors, including Nick Lyons, Ernest Schwiebert, Nicholas Karas, Nelson Bryant, Tom McGuane, and more. Inspirational, funny, and good for you.
Trout Unlimited’s Guide to America’s 100 Best Trout Streams by John Ross – More daydreaming material to read while you’re plotting your next escape.
A Modern Dry-Fly Code by Vincent Marinaro – “Classic and revolutionary book on dry-fly fishing…” Read this before you head to the Letort, Big Spring Creek, Yellow Breeches, Cedar Run, or other Central Pennsylvania limestone streams. That’s where he fished and researched all of this.
The Delaware River and It’s Fisheries – This is a fantastic how-to not just for the Delaware but for targeting freshwater and anadromous species in any river.
Brook Trout: A Thorough Look at North America’s Great Native Trout by Nick Karas – Have to admit I do not own this one, but what would this list be without it? Supposedly a well-researched and interesting work.
Downstream: Reflections on Brook Trout, Fly Fishing, and the Waters of Appalachia by David L. O’Hara and Matthew T. Dickerson – Professors of philosophy and writing combine to pen some wonderful stories about their travels to Eastern brook trout streams. Nicely written and enjoyable reading that will surely remind you of your own trout stream wanderings.