Here is a great little article from MercatorNet, containing "the best 50 opening sentences in English-language fiction." Well, I probably would not say that these are "the best 50" (how do you measure that? from all English literature?), but it is a very neat exercise that you will surely enjoy. You can find below the first part of their list - for the rest, please visit the article itself, if you so desire.
1719, Daniel Defoe, Robinson Crusoe
I was born in the Year 1632, in the City of York, of a good Family, tho' not of that Country, my Father being a Foreigner of Bremen, who settled first at Hull; He got a good Estate by Merchandise, and leaving off his Trade, lived afterward at York, from whence he had married my Mother, whose Relations were named Robinson, a very good Family in that Country, and from whom I was called Robinson Kreutznaer; but by the usual Corruption of Words in England, we are now called, nay we call our selves, and write our Name Crusoe, and so my Companions always call'd me.
1759, Samuel Johnson, The History of Rasselas, Prince of Abissinia
Ye who listen with credulity to the whispers of fancy, and pursue with eagerness the phantoms of hope; who expect that age will perform the promises of youth, and that the deficiencies of the present day will be supplied by the morrow; attend to the history of Rasselas, prince of Abissinia.
1813, Jane Austen, Pride and Prejudice
It is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife.
1830, Edward George Bulwer-Lytton, Paul Clifford
It was a dark and stormy night; the rain fell in torrents--except at occasional intervals, when it was checked by a violent gust of wind which swept up the streets (for it is in London that our scene lies), rattling along the housetops, and fiercely agitating the scanty flame of the lamps that struggled against the darkness.
1843, Charles Dickens, A Christmas Carol
Marley was dead, to begin with. There is no doubt whatever about that.
1850, Charles Dickens, David Copperfield
Whether I shall turn out to be the hero of my own life, or whether that station will be held by anybody else, these pages must show.
1850, Herman Melville, Moby Dick
Call me Ishmael.
1854, Charles Dickens, Hard Times
Now what I want is, Facts.
1859, Charles Dickens, A Tale of Two Cities
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 – in short, the period was so far like the present period, that some of its noisiest authorities insisted on its being received, for good or for evil, in the superlative degree of comparison only.
1865, Lewis Carroll, Alice's Adventures in Wonderland
Alice was beginning to get very tired of sitting by her sister on the riverbank, and of having nothing to do: once or twice she had peeped into the book her sister was reading, but it had no pictures or conversations in it, 'and what is the use of a book', thought Alice, 'without pictures or conversation?'
1890, Arthur Conan Doyle, The Sign of the Four
Sherlock Holmes took his bottle from the corner of the mantelpiece and his hypodermic syringe from its neat morocco case.
1894, Rudyard Kipling, The Jungle Book
It was seven o'clock of a very warm evening in the Seeonee hills when Father Wolf woke up from his day's rest, scratched himself, yawned, and spread out his paws one after the other to get rid of the sleepy feeling in their tips.
1898, H.G. Wells, War of the World
No one would have believed in the last years of the nineteenth century that this world was being watched keenly and closely by intelligences greater than man's and yet as mortal as his own; that as men busied themselves about their various concerns they were scrutinised and studied, perhaps almost as narrowly as a man with a microscope might scrutinise the transient creatures that swarm and multiply in a drop of water.
1900, Frank Baum, The Wonderful Wizard of Oz
Dorothy lived in the midst of the great Kansas prairies, with Uncle Henry, who was a farmer, and Aunt Em, who was the farmer's wife.
1903, Joseph Furphy, Such is Life
Unemployed at last!
1908, Kenneth Graham, The Wind in the Willows
The Mole had been working very hard all morning, spring-cleaning his little home.
1911, James Barrie, Peter Pan
All children, except one, grow up.
1913, Willa Cather, O Pioneers!
One January day, thirty years ago, the little town of Hanover, anchored on a windy Nebraska tableland, was trying not to be blown away.