BC Stillwater flyfishing:
The Gilly (various authors) - this book is the bible and a fun read as well
On Flyfishing the Trout Lakes (Morris & Chan) - a more updated and technical "bible" for our fishery!
Steelhead flyfishing:
A Passion for Steelhead (Hogan) - this is the book that got me super stoked to swing flies for steelhead, and I credit it largely to helping me catch my first on the fly! There are other books on this subject that came out before it and might be more popular (Trey Combs, Bill McMillan, etc), but nothing else I've read stirred up my own "passion" more than this book.
Flyfishing prose:
Seasons of a Fisherman (Haig-Brown) - few books I've read are more poetic and beautifully written than this collection by the man himself. Fantastic read.
Anything by (Gierach) - hilarious almost always, and sometimes quite touching as well.
A River Runs Through It (Maclean) - the story that many credit (or discredit, depending on how you look at it) with creating modern-day flyfishing culture.