With a less talented author, this could be really schlocky (it was black, it was white, it was up and it was down), but instead it is the best of the best. Because it has the right light touch, and it comes off as true:
"It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way.."
A Tale of Two Cities, Charles Dickens

For keeping it real:
"If you really want to hear about it, the first thing you'll probably want to know is where I was born, and what my lousy childhood was like, and how my parents were occupied and all before they had me, and all that David Copperfield kind of crap, but I don't feel like going into it, if you want to know the truth. "
The Catcher in the Rye, J.D. Salinger

For being perfectly ironic:
"It is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife."
Pride and Prejudice, Jane Austen

For painting a sad and beautiful picture with only 25 words:
"To the red country and part of the gray country of Oklahoma, the last rains came gently, and they did not cut the scarred earth."
The Grapes of Wrath, John Steinbeck

For giving you an empty, warped feeling:
"Mother died today. Or yesterday maybe, I don't know."
The Stranger, Albert Camus

For its simplicity:
"It was a pleasure to burn."
Farenheit 451, Ray Bradbury

For making you feel hot, itchy, and like something is off:
"It was a queer, sultry summer, the summer they electrocuted the Rosenbergs, and I didn't know what I was doing in New York."
The Bell Jar, Sylvia Plath

For putting her finger right on it:
"Once upon a time, there was a woman who discovered she had turned into the wrong person."
Back When We Were Grownups, Anne Tyler

For making you take a breath:
"All children, except one, grow up."
Peter Pan, J.M. Barrie

I'm not sure if it's true, but I like it:
"Happy families are all alike; every unhappy family is unhappy in its own way." Anna Karenina, Leo Tolstoy

Not an opening line, but a classic:
"They were careless people, Tom and Daisy - they smashed up things and creatures and then retreated back into their money or their vast carelessness or whatever it was that kept them together, and let other people clean up the mess they had made."
The Great Gatsby, F. Scott Fitzgerald