In reply to Double Knee Bar: I'll swim against the tide a little.
There are a number of books in the classic mountaineering library that I think need to be moved to long-term storage. Patey's One Man's Mountains is terribly dated; though it's a good indicator of what the climbing scene and its personalities was and were like, I don't think it holds up well now (its best essay, A Short Walk with Whillans, is available in the anthology Mirrors in the Cliffs). Joe Brown's The Hard Years similarly; if you want a better indicator of the Rock and Ice scene, then Perrin's Whillans biography The Villain, though flawed, gives a better picture. McFarlane's Mountains of The Mind seems to be acknowledged as a classic; I found it obvious, tedious and badly written and donated my copy to the charity shop as soon as I'd finished it. And I don't think Peter Boardman's books hold up that well either. However, see below.
So what would I recommend? Despite what I've said above, I'd recommend the Boardman Tasker omnibus. This is because it contains Tasker's Savage Arena, which is still a compelling read, and you may as well get the four B-T books in the omnibus if you can. If you can't, get Savage Arena on its own; it's well worth it.
The anthologies The Games Climbers Play and Mirrors in the Cliffs are still good reads, despite now being a little dated. The first contains the eponymous essay by Lito Tejada-Flores and that's still an insightful read; the second contains Robert Reid's marvellous summary of climbing history No Wonder Mallory Didn't Make It. Both contain much else too and the authors contained within may point your reading list in new directions.
Bonington's books are classics; he has his own style and it's easy to mock, but there's a great deal in The Everest Years which is worthwhile. If you want a different take, try Clint Willis' The Boys of Everest - but you might want to have a look at this thread first
http://www.ukclimbing.com/forums/t.php?t=212824
If Everest interests you, try Walt Unsworth's Everest; a marvellous book. Still in the greater ranges, try Greg Child's Thin Air.
More when they come to me...have fun reading.
T.