Here's an example from Philipp Meyer's 2013 novel The Son (a book that I really want to re-read sometime in 2016):
Opening sentence: "It was prophesied I would live to see one hundred and having achieved that age I see no reason to doubt it."
Closing sentence: "As far as I know he is looking for me yet."
Doesn't that make you want to find out what happened to this old person in between those two sentences?
Or how about this from a book that introduces some of my very favorite characters of all-time (and that plot...wow).
Opening sentence: "When Augustus came out on the porch the blue pigs were eating a rattlesnake - not a very big one."
Ending sentence: "They say he missed that whore."
Right from the get-go, I knew I had not picked up a run-of-the-mill Western because Larry McMurtry set the irreverent tone that would be present throughout the rest of the book's 843 pages. I was hooked.
And then there's this from the book that turned me into a lifelong reader of John Irving's fiction:
First sentence: "Garp's mother, Jenny Fields, was arrested in Boston in 1942 for wounding a man in a movie theater."
Ending sentence: "But in the world according to Garp, we are all terminal cases."
It is pretty evident that the odds that Garp has had a normal childhood and life are pretty low ones. Whose fault is that going to be, his or his mother's? And just how weird is this going to get (pretty weird, as it turns out)?