Weinberg, Steven: The First Three Minutes
Contemporary science writing by a Nobel Prize-winning physicist, which explains to general readers what happened when the universe began, and how we know. A superb book, which is rapidly (and justifiably) attaining the status of a classic.
Al-Khalili, Jim: Black Holes, Wormholes and Time Machines
A superb book which will appeal to anyone from interested teenager to someone well-versed in physics and cosmology. Al-Khalili is the pre-eminent populariser of the physical sciences in Britain today and this entertaining and exceptionally well written book, which makes no concessions to "dumbing down", shows why. This new (2011) edition incorporates recent findings in cosmology and partical physics.
Al-Khalili, Jim: Quantum: A Guide for the Perplexed
Eight years after publication, this is still the best introduction to Quantum Physics for the general reader. This very well-written book untangles the weirdness of the quantum world, explains the theories, explores their consequences and presents a cutting-edge guide to the current state of the science. (A new edition is due to be published later this year.)
Gribbin, John: Companion to the Cosmos
Although it is now difficult to obtain, this is an excellent reference, arranged alphabetically and is thoroughly worth getting.
Gribbin, John: In Search of the Big Bang
Another Gribbin book that can be difficult to obtain, this is easily the best introduction to Big Bang for the beginner. Very well written and explained. However, if you are already well-read in cosmology, this basic primer is probably not the book for you.
Guth, Alan: The Inflationary Universe: The Quest for a New Theory of
Very well-written autobiographical account of Guth's development of the theory of Inflation, which is fundamental to our current understanding of the Big Bang.
Hartquist, T.W. and Williams, D.A.: The Chemically Controlled Cosmos
An introduction to cosmic chemistry for the non-specialist. Essential reading if you wish to understand our origins.
Verschuur, Gerrit L. : The Invisible Universe Revealed: The Story of Radio Astronomy
Excellent account of the story of radio astronomy, this well illustrated and very readable book is an excellent introduction to the ideas, discoveries and techniques in this field.