Fortunately, there are a few authors who know what they're talking about. John Gribbin, who wrote In Search of Schrödinger's Cat two decades ago, followed up with the sequel Schrödinger's Kittens and the Search for Reality.
A recent alternative to Gribbin's books is Quantum Enigma by Rosenblum and Kuttner. This book has less history than In Search of Schrödinger's Cat but more philosophy and more emphasis on the implications for consciousness. (The book's subtitle is "Physics Encounters Consciousness.") Clear examples are given. A paperback edition is due out in June 2008.
If you get through those books and want more, or if you want a more challenging (yet still non-mathematical) starting point, try David Albert's Quantum Mechanics and Experience. This book is incredibly clear and illuminating, so long as you have the mental fortitude to work through the logic of some rather long multi-clause sentences. If you're already used to reading demanding prose -- prose for which you sometimes have to reread a paragraph once or twice before its meaning becomes entirely clear -- then this book can't be beat.
The most successful version of quantum mechanics, called "quantum electrodynamics" (QED), combines quantum ideas with Einstein's special relativity. One of the co-discoverers of QED (and co-Nobel-prize-winners), Richard Feynman, wrote a short, light, clear description called QED. There's no math at all, just pictures and conversational text, but Feynman explains why this doesn't entail a diluted treatment of the subject.
Both Gribbin and Paul Davies write about all aspects of modern "natural philosophy," including quantum mechanics, time, and the relationship of science to religion. Amit Goswami is another author who writes about science and religion, coming at it from a Hindu background. Here one leaves the realm of "inferences supported by experimental data" and enters that of "educated speculation" -- but so long as you recognize that, you can profitably read these works.