I suppose that it depends on what you are looking for. If you have little or no prior experience with the subject and you simply wish to find out why it is claimed that the evidence is overwhelming - in effect, to familiarize yourself with the subject, and to gain a very basic understanding - then I would certainly recommend Jerry Coyne's book. I haven't read Richard Dawkins new book, as yet, so I cannot say which is better.
Donald Prothero's book, "What the Fossils Say and Why it Matters" is also excellent for the "layperson", because it contains some explanation of the history of creationism, geology, and why creationism is not taken seriously. However, while the book does include explanations of other branches of evolutionary science, it is, as the title suggests, largely focused on the fossil evidence.
In all honesty, if someone wanted to both present the evidence in full, as well as the logic (and by logic, I mean the reason that the theory and explanations make sense in light of the evidence), then it would require a book that was tens of thousands of pages! It is always important to remember that, because one book - not even a textbook - can fully do justice to what is an enormously rich and detailed subject.
If I had to pick one, then it would have to be the book that started it all; "On the Origin of Species" by Charles Darwin. It's actually surprisingly readable and was, in its own time a "popular science" book. It's also interesting how hollow and transparently feeble many of the objections to Darwin and his theory that are touted today become when you've actually read it for yourself.
Fortunately, we don't have to restrict ourselves, and some of my other favourites would be "The Diversity of Life" by E. O. Wilson, pretty much anything by Dawkins; "The Selfish Gene", "The Blind Watchmaker", "Climbing Mount Improbable" and "The Ancestor's Tale" are all excellent. Ditto for Stephen Jay Gould, "Bully for Brontosaurus" I think was the first Gould I ever read and remains one of my favourites.
Some of the more recent offerings such as "Why Evolution is True" by J. Coyne and the aforementioned "Evolution: What the fossils say and why it matters" are also excellent and well worth getting stuck into.
I think I would need to know a little more about the what the potential reader wanted.
If someone wants answers to those important questions "where did we come from?", "how did we get here?", I would recommend The Ancestor's Tale: A Pilgrimage to the Dawn of Life. It tackles those questions in a unique way that enables the reader to decide how far to pursue the answers, by working backwards through time.
First of all, thanks for your all you thoughtful and useful answers.
"What the Fossils Say and Why it Matters" and "Bully for Brontosaurus" are both new titles to me and I've also been encouraged to add "Your Inner Fish" to my reading list.
I'm inclined to agree that if it was a matter of being stuck on a desert island then "Origin of Species" (which I have read) would probably be the best choice - partly because you'd have time to read it and partly because it would probably encourage you to observe your surroundings. Come to think of it, it's probably the ideal "Desert Island Discs" book choice (especially if you've already got the Bible and Shakespeare).
Seriously folks, try 'Almost Like a Whale' by Steve Jones. An excellent update of Darwin's therioes and much easier to read. Of course, I may be biased. He was my tutor at University College London where he is now Professor of Genetics. Doubt he remembers me though!