Read Brian Greene's The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory., and then watch the Nova program based on the book that aired on PBS. Although a few years old, most of what it says remains accurate. Also read his more recent books The Fabric of the Cosmos: Space, Time and the Texture of Reality and The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos. All are really good reads.
Black Holes and Time Warps: Einstein's Outrageous Legacy by Kip Thorne. Everything from Einstein to Hawking and beyond. Relativity, and how it must be reconciled with quantum mechanics to achieve a true understanding of the Universe. He also goes beyond to some very speculative physics relating to time warps and worm holes, although both of these ideas do have a basis in relativity theory. Includes a number of personal anecdotes which I feel add to the book; some people, I know, disagree.
Lee Smolin's book Three Roads to Quantum Gravity explores String Theory, "M" Theory and Loop Quantum Gravity (LQG). It proposes that all three are approximations to a single underlying theory. An interesting man, he gets very frustrated that String and "M" theory get by far the largest share of particle physics research, and that his pet theory (LQG) gets very little, as discussed in another of his books The Trouble with Physics, which I would not particularly recommend.
Michio Kaku is a well known popularizer of science, and most of his books are a good read. I particularly like Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. It is another book that addresses the reconciliation of Relativity and Quantum Mechanics, and is one of the best at explaining the "how" and "why" of multi-dimensional space; for example why String Theory is formulated in ten dimensions.
John Gribbin's 1984 book In Search of Schrödinger's Cat: Quantum Physics And Reality is the best introduction to the whole of quantum physics. While it does not cover some of the latest discoveries, like quantum entanglement, all the basic necessities are there. In Search of the Big Bang is another excellent read. Cosmic Coincidences: Dark Matter, Mankind, and Anthropic Cosmology, written in 1989 with Martin Rees, now Astronomer Royal in the UK, is also quite interesting as an introduction to the Anthropic Principle. It is a very well written book, containing a wealth of information. Personally, I see very little relevance in the anthropic principle; you may disagree.
Lisa Randall's book Warped Passages: Unraveling the Universe's Hidden Dimensions, published in 2005. Where most multi-dimension proposals posit microscopic extra dimensions, possibly on the Planck length scale, she proposes large, possibly infinite extra dimensions. These ideas may explain why gravity is so weak compared to electromagnetism and the other forces of nature. In reality, the subject matter is complex and heavily mathematical, but her use of allegory makes getting to the core of what she is saying logical and fun. Also, for the first time, we have a theory that could be explored experimentally using the LHC. A jolly good read. Her second book, Knocking on Heaven’s Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World, is also recommended.
Steven Weinberg's The First Three Minutes: A Modern View of the Origin of the Universe is an absolute classic. Though first published back in 1977, it remains one of the very best descriptions of the very early Universe for the intelligent lay person. His other books are also excellent; for example, Dreams of a Final Theory: The Search for the Fundamental Laws of Nature.
Bill Bryson's book A Short History of Nearly Everything is a very witty journey through science, not just physics. Very funny, and very illuminating. I have read many of his books and they are all recommended.
Another beautifully written, witty and entertaining, book is The God Particle: If the Universe is the Answer, What is the Question? by Leon Lederman and Dick Teresi. The book does do a great job of advertising the importance of the Superconducting Super Collider, but as this was not built, just translate it into the Large Hadron Collider in your mind! Although Lederman gave the Higgs Boson the title "God Particle", and this has been taken up enthusiastically by the media, scientists generally do not like the name preferring to retain Higgs Boson.
I have read many of Nigel Calder's books and would definitely recommend The Violent Universe (1969) and The Restless Earth (1972), but all of his books represent a good read. Do not be put off by the fact that many are quite old now. It is useful to see at how science looked in the past compared to today; and much has changed very little in broad concept! However, I would avoid any of his writing on climate change. His views are, to me, very strange.
James Gleick's Chaos: Making a New Science is an excellent introduction to chaos theory.
No list would be complete without Surely You're Joking, Mr. Feynman! Just read it for fun, then read James Gleick's book Genius: The Life and Science of Richard Feynman.
Here are a few of the books about science that I enjoy. I include only books that I have read at least twice. If it was not worth re-reading, it did not make the list!