Harry Harrison’s Captive Universe is an excellent one … I was going to tell you all about it but the whole post would be a spoiler block 
I read a very cool one a while ago, by Ursula K. LeGuin, I think. I can’t remember if it was in a book I got from the library, or one I own, and I’ve got books everywhere, so I can’t readily look for it if it is one I own. I really need to buy an additional bookcase, except I don’t have anywhere to put one in my current place. At any rate it was set on a ship that was thought to be at the mid-point of its journey, i.e several generations had passed since departure, and several more were expected to pass before arrival. Because there was no longer anyone alive who had been on Earth, many people were coming to believe that it was just a myth, as was the final destination, and the ship was the only reality. It was then discovered that the ship was going faster than anyone thought, due to a gravitational effect, IIRC, and was going to arrive at its destination within a year or two, resulting in a struggle between the people who were excited about arriving and the people who thought the ship was the only reality. Can anyone confirm who wrote this story and what it’s called?