It was 1968, and I remember sitting in a theater in Santa Barbara with my grandmother when this movie's plot twist was revealed in the final frames. I know my jaw must have visibly dropped, so taken in was I. To me, one of the best plot twists in movie history. Far be it from me to be a plot spoiler and name the flick, but I think most folks will recognise it without having it named.
The flick that failed to surprise me, but which a lot of people name as having cinema's best plot twist, was The Sixth Sense. I was prepared for the ending, as my wife had speculated the plot had been lifted from a Goosebumps book she had read to our kids years before. Sat through that movie with her prediction running through my head, and sure enough... Talk about a spoiler.
Peace to all you folks, and be safe and sane for Independence Day.