I think you really need to define "spoiler" better.

If "spoiler" means "thing that people going into the movie are not expected to know", then everything has lots of them.

If "spoiler" means "revelation of critical plot point, which is built to by author of work, which diminishes the rest of the movie if revealed to the viewer BEFORE that point", then your suggestion list needs to shrink, a lot.

Since we're only listing classics, that shrinks us further.

> Citizen Kane

Can do.

> Star Wars

Sure.

> The Usual Suspects

Okay.

> Soylent Green

Not particularly avoidable, but sure, knowing it's people ruins most of the build. Okay.

> The Sixth Sense

It's the point of the movie, so okay.

> War Of The Worlds

No. The story is still the same, regardless of the Deus Ex Virii.

> The Crying Game

Yes.

> Final Fantasy VII

Knowing that Cloud is a clone does not change this game.

> Fight Club

Yes.

> Psycho

Yes.

> Harry Potter

Uh, no. Children's books, especially children's mysteries, always rely on the sudden twist.

> Memento

Knowing Joey Pants' story doesn't invalidate the rest of the movie.

> Babylon 5

Classic and large, remember?

> Spartacus

#1: Not a spoiler because it's not a secret.
#2: Not a spoiler because it doesn't spoil the story.

> Escaflowne

Including this would imply that there is something to spoil.

> Watchmen

I'd take it off, because it's limited to the trivial subset of "comic book geeks", and hence doesn't fit any of the mainstreaming requirements