I'm pleased to see Pride and Prejudice made it into the comments, it's still one of my favourites, and indicates my preference.
Too many, too often, seem to be trying too hard. They sound like they're trying to be their own epigraph rather than a true part of the text. The ones that work best (for me) are the ones that feel like a natural part of what follows, they just happen to be also significant on their own. (As is the case with Pride and Prejudice).
A contrary example (from the link), is something like this one:
Happy families are all alike; every unhappy family is unhappy in its own way.
-- Leo Tolstoy, Anna Karenina
I do like what this says, but it doesn't (to me) really feel like part of the text. It could have been put on a page on its own out front somewhere. It was something written to be a first line, and it could be a first line to a wide assortment of books.