Perhaps the most famous (to this crowd!) example of a plot twist would be from Star Wars Episode V: The Empire Strikes Back when Darth Vader tells Luke: "I am your father." However, I maintain this wasn't done in the ideal manner; the creator lied to the audience, i.e. prior to this scene, Obi-Wan and Luke's aunt and uncle have all told Luke his father is dead.
Why are twists good? Plot twists are good because we all (including editors!) want to read something fresh. We're tired of the same old, same old. As the fabulous Robert Silverberg said, ...the basis of all the successful and lasting narrative of the past five thousand years ...[is] A sympathetic and engaging character (or an unsympathetic one who is engaging nevertheless), faced with some immensely difficult problem that it is necessary for him to solve, makes a series of attempts to overcome that problem, frequently encountering challenging sub-problems and undergoing considerable hardship and anguish, and eventually, at the darkest moment of all, calls on some insight that was not accessible to him at the beginning of the story and either succeeds in his efforts or fails in a dramatically interesting and revelatory way, thereby arriving at new knowledge of some significant kind.
Bring on the twists!