Godfather and Apocalypse Now are definitely in there.
After that, I'm not sure. Probably some of Casablanca, The Third Man, Double Indemnity, Once Upon A Time In The West, Blade Runner, and Heat, or maybe something from Hitchcock (Rear Window? North By Northwest? Notorious?) or one out of It's A Wonderful Life, The Maltese Falcon, Chinatown, The Pianist, La vita è bella, The Eternal Sunshine Of The Spotless Mind, and Children Of Men. And maybe Citizen Kane once I've rewatched it.
I don't know how people can ever choose.