Taking a break from what's threatening to become an obsession...
What you're trying to do is give them a sense of who we are---your take on our dreams, our attitudes, our idioms, what we think we are, what we are afraid we are, what we really might be.
Sheila put her list together to include the light and the dark, so it includes His Girl Friday and Bonnie and Clyde, Taxi Driver and Field of Dreams. But there aren't rules and you can go with all one or the other, if you want, a list of Disney's Greatest Hits, the best of Martin Scorcese, all Howard Hawks, or the best of Jerry Lewis.
I'll post my own list in the morning. Got to think some more. It's going to have a Western on it, I know that. But a Western by virtue of its being a Western is expressive. What I need is a Western that a great example of the genre and says something about being an American. So Stagecoach won't make the list but The Searchers might, even though, blasphemy, I think Stagecoach is really the greater Western.
Add your own suggestions in the comments or post them on your blogs.