Objectively concerning physical evidence of the Book of Mormons validity:
The "evidences" listed by jgardn above are the kind of things Mormons come up with to ease their minds when confronted with the facts science has uncovered regarding the Book of Mormon. These facts are usually simply never discussed by Mormons, except rarely when in the context of providing an attempt at refutation (see above). Notice that jgardn's evidences (quetzlcoatl, hopi weapons) are not really evidences, but stories and speculation that make one say "Hmmm, that's interesting, maybe the Book could be true". If that kind of thing is all you read, you'll become a believing Mormon too. However, there's a lot better "evidence" available, and when considering it all the Book doesn't fare too well.
In fact, there have been successful refutations of the Book of Mormon's claims; the overwhelming preponderance of evidence suggests that the Book of Mormon is a nineteenth-century work of fiction, when looked at objectively. You can show Mormons an endless stream of historical, geographical, linguistic and genetic evidence proving that the Book of Mormon cannot be what it says, and they will all say the same thing jgardn say in his/her last sentence: "I don't care what you say, I asked God and he told me it's true."
Fine for them, but for those who demand a little more rigor in the test for truth than "God told me so", here is a page that lists several problems with the book. Stories and speculation do little to answer these issues, especially when taken together as a whole as they should be:
http://www.lds-mormon.com/bookofmormonquestions.shtml