Perhaps adding spoiler tags for Soylent Green or Sixth Sense would be a little silly, but in general, it's common courtesy to alert the reader in case they care (and it's not like it costs you anything).
I really hate it when I people give away spoilers. Like when I read something that casually gave away the ending of The Usual Suspects, which I'd been looking forwards to seeing.
I recently read The Man Who Was Thursday by G.K. Chesterton – a thriller that I ran across a spoiler to years and years ago and was hoping I would forget. Eventually I had to admit I never would and read the book. I enjoyed it anyway.
The Kids in the Hall used to have a couple of comedy characters whose schtick was that they were trying hard to be evil but could only ever manage to be a little bit evil. One of the only-sort-of-evil things the characters did was give away the endings to movies. A friend told me that he saw them perform it live, and they picked some movie that had only just come out and actually gave away the ending. The entire audience yelled "Evil!" I thought it was taking the joke much too far.