1. "Happy families are all alike; every unhappy family is unhappy in its own way." - Leo Tolstoy's Anna Karenina
This one isn't exactly fair. It's a translation from Russia. Assuming the meaning was taken as closely as possible, it isn't a particularly good opening. For one, there's a semi-colon. Who does that? Second, it's so ambiguous it's outputting. (Feel free to express dissent.)
2. "It was a bright cold day in April, and the clocks were striking thirteen." - George Orwell's 1984
The use of a comma and "and" throws this off a little. Other than that, the sentence is intriguing and suave, two perfect attributes for an opener.
3. "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." - Charles Dickens' A Tale of Two Cities
I do not appreciate the length.
4. "Somewhere in la Mancha, in a place whose name I do not care to remember, a gentleman lived not long ago, one of those who has a lance and ancient shield on a shelf and keeps a skinny nag and a greyhound for racing." - Miguel de Cervantes' Don Quixote
The use of 3rd-narrative to give an instant impression of the protagonist is brilliant.
5. "All this happened, more or less." - Kurt Vonnegut's Slaughterhouse-Five
I wonder if the narrator is going to be a little unreliable? Hmm...I'm going to say "yes". This opener really makes you feel like you've opened a book.