I'm really not big on philosophy/critical analysis being all that important in one's personal library. But I can recommend The Nature of Photographs: A Primer by Stephen Shore.
I second the recommendation of "The Photographers Eye", and "Looking at Photographs". Also "Pictorialism to Modernism" which is an excellent illustrated discussion of photographers. and processes in the 1st half of the century.
[FONT=Comic Sans MS]Films NOT Dead - Just getting fixed![/FONT]
Nothing I can recommend, but maybe of interest to you:
A book I have enjoyed rereading many times is " The New Vision" by Maria Morris Hambourg from the Metropolitan Museum of Art. While it seems to follow the usual "everything follows Stieglitz" trend, a careful reading allows a line through Clarence Whites' Students to the Modernism of the 1920's and 30's. Christoper Phillips essay is good and makes me want to get a copy of his "Photography in the Modern Era: European Documents and Critical Writings, 1913-1940 "
"There are a great many things I am in doubt about at the moment, and I should consider myself favoured if you would kindly enlighten me. Signed, Doubtful, off to Canada." (BJP 1914).
Maybe the Aperture anthology edited recently can be part of your to-read list? The selection of articles is pretty wide to cover multiple aspects of photography.
"The problem with photography is that it only deals with appearances." Duane Michals
"A photograph is a secret of a secret. The more it tells you the less you know." Diane Arbus
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Oh well, didn't have time to reply yesterday; but then I thought if I wait a bit, I'll just have to second the obvious.
On my own shelf, and all well thumbed--
Sontag (both titles; look up the other one)
--most were mentioned before.
For a masterpiece of a critical monograph, Looking in Robert Frank's The Americans. Kozloff's Theatre of the Face for a more encyclopaedic approach to one specific niche.
But if you really want to feel 20th century photography, nothing will beat getting and fondling, night after night, some of the monumental, seminal works of the period--Nachtwey's Inferno, Smith's Minamata, Salgado's Sahel, Koudelka's Gypsies...
Pretty much anything by Depardon, if you read French, combined with some rambling, incoherent thinking of your own, will give you great into the roots, the very heart of the published-back-then image: the mind of the photographer.
These just for starters...
Besides the outstanding, if not "mandatory" 20th Century suggestions above, try these on for size (I still revisit them in my home library, often):
"The Camera Viewed: Writings on Twentieth-Century Photography", Vols 1 & 2 (Softbound), edited by Peninah R. Petruck.
"Photography in Print: Writings from 1816 to the Present", edited by Vicki Goldberg.
"Diana & Nikon", by Janet Malcolm.
"A World History of Photography", by Naomi Rosenblum.
"American Photography: A Critical History 1945 to the Present", by Jonathan Greene.
"Looking at Photographs", by John Szarkowski.
"Aperture Magazine Anthology: The Minor White Years, 1952-1972", edited by Peter Bunnell (recently published).
Essay: "The Work of Art in the Age of Mechanical Reproduction" by Walter Benjamin.
In addition, seek out every monograph (of interest).