What are some old films for people who hate old films?

This (somewhat) egotistically worded question comes directly from a message board on IMDB:

“We’ve all encountered people who say that they don’t like older films, for one poor reason or another. Even though I shouldn’t be, I’m always a little bit surprised by this attitude, since it should be obvious that a film’s age shouldn’t in and of itself determine its quality, and it seems crazy to me to lump all “old movies” together as uniformly “bad” or “not my taste.”

What are some films from, say, 1960 and earlier which you would recommend to people who are convinced that old movies suck? In other words, which films do you think could change their minds and help them see the error of their ways? So, don’t just list great movies, try to name films that would make someone who hates old movies admit, “Yeah, that’s pretty cool.”

Here are some I would personally recommend:

Singin’ in the Rain
Sunset Boulevard
The Apartment
All About Eve
Marty
Strangers on a Train
The Day the Earth Stood Still